Question

How do you combine real and imaginary numbers?

Answer 1

Combine real and imaginary numbers:

Real parts with imaginary parts can't combine by using addition or subtraction, because they're not like terms,

so you have to keep them separate but we can write them together.

When a real number and an imaginary number are combined to form a complex number.

It is represented by:

$Z=a+ib$

where,

$i$ represent imaginary part

$a$ and $b$ are integers

For example:

Let $3+2i$ and $2-5i$be two complex numbers.

By combinations of real numbers and imaginary numbers, we can perform algebraic operations on them

But the real number will do operations with real numbers and imaginary with imaginary numbers.

Let $Z_1=3+2i$ and $Z_2=2-5i$

Now, $Z=Z_1+Z_2$

$\begin{array}{rcl}Z& =& (3+2i)+(2-5i)\\ & =& 3+2i+2-5i\\ & =& (3+2)+i(2-5)\\ & =& 5-3i\end{array}$

Hence, a real number and an imaginary number, when combined (or written together ) form a complex number.