double abs(complex)
Returns the absolute value or magnitude of its argument. The absolute value of a complex value (a, b) is the positive square root of a2 + b2.
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double abs(const complex&)
Returns the absolute value or magnitude of its argument. The absolute value of a complex value (a, b) is the positive square root of a2 + b2.
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double arg(complex)
Returns the angle (in radians) of the polar representation of its argument. If the argument is equal to the complex number (a, b), the angle returned is the angle in radians on the complex plane between the real axis and the vector (a, b). The return value has a range of -pi to pi.
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double arg(const complex&)
Returns the angle (in radians) of the polar representation of its argument. If the argument is equal to the complex number (a, b), the angle returned is the angle in radians on the complex plane between the real axis and the vector (a, b). The return value has a range of -pi to pi.
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complex conj(complex)
Returns the complex value equal to (a, -b) if the input argument is equal to (a, b).
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inline complex conj(const complex&)
Returns the complex value equal to (a, -b) if the input argument is equal to (a, b).
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complex cos(complex)
Returns the cosine of the complex argument.
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complex cos(const complex&)
Returns the cosine of the complex argument.
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complex cosh(complex)
Returns the hyperbolic cosine of the complex argument.
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complex cosh(const complex&)
Returns the hyperbolic cosine of the complex argument.
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complex exp(complex)
Returns the complex value equal to e to the power of x where x is the argument.
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complex exp(const complex&)
Returns the complex value equal to e to the power of x where x is the argument.
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double imag(const complex&)
Extracts the imaginary part of the complex number provided as the argument.
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inline double imag(const complex&)
Extracts the imaginary part of the complex number provided as the argument.
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complex log(complex)
Returns the natural logarithm of the argument x.
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complex log(complex)
Returns the natural logarithm of the argument x.
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double norm(complex)
Returns the square of the magnitude of its argument. If the argument x is equal to the complex number (a, b), norm() returns the value a2 + b2.
norm() is faster than abs(), but it is more likely to cause overflow errors.
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double norm(const complex&)
Returns the square of the magnitude of its argument. If the argument x is equal to the complex number (a, b), norm() returns the value a2 + b2.
norm() is faster than abs(), but it is more likely to cause overflow errors.
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int operator !=(complex, complex)
The inequality operator "!=" returns a nonzero value if x does not equal y. This operator tests for inequality by testing that the two real components are not equal and that the two imaginary components are not equal.
Because both components are double values, the inequality operator returns false only when both the real and imaginary components of the two values are identical. If you want an inequality operator that can test for an absolute difference within a certain tolerance between the two pairs of corresponding components, you can use a function such as the is_not_equal function.
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inline int operator !=(const complex&, const complex&)
The inequality operator "!=" returns a nonzero value if x does not equal y. This operator tests for inequality by testing that the two real components are not equal and that the two imaginary components are not equal.
Because both components are double values, the inequality operator returns false only when both the real and imaginary components of the two values are identical. If you want an inequality operator that can test for an absolute difference within a certain tolerance between the two pairs of corresponding components, you can use a function such as the is_not_equal function.
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complex operator *(complex, complex)
The multiplication operator returns the product of x and y.
This operator has the same precedence as the corresponding real operator.
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complex operator *(const complex&, double)
The multiplication operator returns the product of x and y.
This operator has the same precedence as the corresponding real operator.
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complex operator *(const complex&, const complex&)
The multiplication operator returns the product of x and y.
This operator has the same precedence as the corresponding real operator.
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complex operator +(complex, complex)
The addition operator returns the sum of x and y.
This operator has the same precedence as the corresponding real operator.
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inline complex operator +(const complex&, const complex&)
The addition operator returns the sum of x and y.
This operator has the same precedence as the corresponding real operator.
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inline complex operator -(const complex&, const complex&)
The subtraction operator returns the difference between x and y.
This operator has the same precedence as the corresponding real operator.
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complex operator -(complex, complex)
The subtraction operator returns the difference between x and y.
This operator has the same precedence as the corresponding real operator.
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inline complex operator -(const complex&)
The negation operator returns (-a, -b) when its argument is (a, b).
This operator has the same precedence as the corresponding real operator.
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complex operator -(complex)
The negation operator returns (-a, -b) when its argument is (a, b).
This operator has the same precedence as the corresponding real operator.
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complex operator /(const complex&, double)
The division operator returns the quotient of x divided by y.
This operator has the same precedence as the corresponding real operator.
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complex operator /(const complex&, const complex&)
The division operator returns the quotient of x divided by y.
This operator has the same precedence as the corresponding real operator.
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complex operator /(complex, complex)
The division operator returns the quotient of x divided by y.
This operator has the same precedence as the corresponding real operator.
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int operator ==(complex, complex)
The equality operator "==" returns a nonzero value if x equals y. This operator tests for equality by testing that the two real components are equal and that the two imaginary components are equal.
Because both components are double values, the equality operator tests for an exact match between the two sets of values. If you want an equality operator that can test for an absolute difference within a certain tolerance between the two pairs of corresponding components, you can use a function such as the isequal function.
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inline int operator ==(const complex&, const complex&)
The equality operator "==" returns a nonzero value if x equals y. This operator tests for equality by testing that the two real components are equal and that the two imaginary components are equal.
Because both components are double values, the equality operator tests for an exact match between the two sets of values. If you want an equality operator that can test for an absolute difference within a certain tolerance between the two pairs of corresponding components, you can use a function such as the isequal function.
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complex polar(double, double = 0)
Returns the standard complex representation of the complex number that has a polar representation (a, b).
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complex pow(complex, double)
Returns the complex value xy, where x is the first argument and y is the second argument.
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complex pow(double, complex)
Returns the complex value xy, where x is the first argument and y is the second argument.
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complex pow(complex, complex)
Returns the complex value xy, where x is the first argument and y is the second argument.
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complex pow(complex, int)
Returns the complex value xy, where x is the first argument and y is the second argument.
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complex pow(const complex&, int)
Returns the complex value xy, where x is the first argument and y is the second argument.
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complex pow(const complex&, double)
Returns the complex value xy, where x is the first argument and y is the second argument.
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complex pow(const complex&, const complex&)
Returns the complex value xy, where x is the first argument and y is the second argument.
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complex pow(double, const complex&)
Returns the complex value xy, where x is the first argument and y is the second argument.
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double real(const complex&)
Extracts the real part of the complex number provided as the argument.
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inline double real(const complex&)
Extracts the real part of the complex number provided as the argument.
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complex sin(const complex&)
Returns the sine of the complex argument.
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complex sin(complex)
Returns the sine of the complex argument.
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complex sinh(const complex&)
Returns the hyperbolic sine of the complex argument.
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complex sinh(complex)
Returns the hyperbolic sine of the complex argument.
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complex sqrt(complex)
Returns the square root of its argument. If c and d are real values, then every complex number (a, b), where:
a = c2 - d2 b = 2cd
has two square roots:
(c, d) (-c, -d)
sqrt() returns the square root that has a positive real part, that is, the square root that is contained in the first or fourth quadrants of the complex plane.
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