Question

What is a complex number? Give an example of a complex number, and identify the real and imaginary parts.

Short answer

Complex number is a number that is the combination of real and imaginary part. In general complex number can be expressed as $a+ib$, an example of complex number is$z=5+4i$ in which the real part is$5$ and the imaginary part is $4i$.

Step-by-step solution

Step 1. Define complex number.

Complex number is a number that is the combination of real and imaginary part. In general complex number can be expressed as $a+ib$.

Here, aand b are real number and i is the imaginary number.

Step 2. Define imaginary number.

Imaginary number is the solution of the equation of$x^2=-1$ and there is no real number which satisfies this equation.

Consider the equation.

$x^2=-1$

Take square root on both sides.

$\begin{array}{c}\sqrt{x^2}=\sqrt{-1}\\ x=\sqrt{-1}\\ =i\end{array}$

The value of the imaginary number is $i=\sqrt{-1}$

Step 3. Depict the imaginary number mathematically.

Example of complex number is,

$z=5+4i$

Here, the real part is$5$ and the imaginary part is $4i$.

Thus, complex number is a number that is the combination of real and imaginary part. In general complex number can be expressed as $a+ib$, an example of complex number is$z=5+4i$ in which the real part is$5$ and the imaginary part is $4i$.