<complex>

The <complex> header file implements the complex class to contain complex numbers in cartesian form and several functions and overloads to operate with them. Simply stating, the <complex> header file helps to deal with complex numbers. A complex number can be defined as follows.

complex <arg_type> sample(arg1, arg2);

If c is a complex number,

Method	Description
real(c)	Real Part of c
imag(c)	Imaginary Part of c
abs(c)	Magnitude of c
arg(c)	Amplitude of c
conj(c)	Complex Conjugate of c

And, the arithmetic operators +, -, *, / are overloaded so that they can be directly used to add two complex numbers.

This code can be used to perform arithmetic on two complex numbers.


	            complex <double> a(1, 2), b(3, 4);

                cout << "Addition : " << a + b << endl;

                cout << "Subtraction : " << a - b << endl;

                cout << "Multiplication : " << a * b << endl;

                cout << "Division : " << a / b << endl;

It outputs the results of addition, subtraction, multiplication and division of two complex numbers (1 + 2i) and (3 + 4i) [Try It Yourself!].

In addition, polar(ρ, θ) can be used to convert the complex number from polar form to cartesian form.

Fill in the Blanks

The header file is used to deal with complex numbers in C++.

Complex Number Functions

Here is a list of some complex number functions provided by the <complex> header file.

Function	Description
sqrt(c)	Square Root of c
exp(c)	Exponential of c
log(c)	Natural Logarithm of c
log10(c)	Common Logarithm of c
sin(c)	Sine of c
cos(c)	Cosine of c
tan(c)	Tangent of c
asin(c)	Inverse Sine of c
acos(c)	Inverse Cosine of c
atan(c)	Inverse Tangent of c
sinh(c)	Hyperbolic Sine of c
cosh(c)	Hyperbolic Cosine of c
tanh(c)	Hyperbolic Tangent of c
asinh(c)	Inverse Hyperbolic Sine of c
acosh(c)	Inverse Hyperbolic Cosine of c
atanh(c)	Inverse Hyperbolic Tangent of c

Here, c is a complex number. Using the <complex> header, different kinds of complex number functions can be performed (Try It Yourself!).

Fill in the Blanks to output the common logarithm of complex number 'c'.

cout << << endl;

<complex> - C++ header