# Sum and Product of Complex Numbers

## Sum and Product of Two Complex Numbers

When do we say that two complex numbers are equal? How do we solve complex numbers?

In this lesson, you must be able to:

- Define equality of complex numbers
- Solve complex numbers

To add or multiply two complex numbers, we consider them as if they were polynomials. Simplify the result by letting *i ^{2 }= *-1.

Examples:

Find the sum and product of the complex numbers *5 - 4i* and *- 2 + 6i.*

Find the QUOTIENT of *1/(4-3i).*

* *

To do so, multiply the numerator and denominator by the conjugate of the denominator.

* *

The final answer is in standard form.

*Summary:*

- Two complex numbers a+bi and
*c+di*are said to be equal if and only if*a=c*and*b=d.* - To add or multiply two complex numbers, consider them as if they were polynomials and simplify the result by letting
*i*^{2 }*= -1.* - To divide two complex numbers, multiply the expression by the conjugate of the denominator.

## Comments

**George Dimitriadis** from Templestowe on October 17, 2020:

Hi

You have provided a good summary of the basic properties of complex numbers.

The example for Product has + between the brackets instead of x.

I'm not sure what prerequisite knowledge your article assumes. Perhaps you should define what a conjugate is, and the definition of a complex number more precisely, such as:

z=a+bi, where a, b are real numbers and i^2=-1.

Another suggestion is that you might consider inserting the practice questions in a quiz module so that the reader can check teir answers.