Complex Numbers Problems and Solutions

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This is one in a series of Math resources you’ll find in this site. In this article, we hope to clear up common complex numbers problems. They aren’t called complex for no reason but, as with all other math problems, these have solutions.

What are complex numbers?
First, it’s best to be cleared about complex numbers. Not too long ago, mathematicians of all time devised a complete number system that includes both real and imaginary. Numbers in this system are called complex numbers. These numbers is composed of all sums a + bi where a and b are real numbers and i is imaginary.

Real numbers belong to the complex number system because a = a + Oi.

I acts as would any other variable, such as:

Ex.
Problem: 7i + 9i
Solution: combine like terms.
16i

Like real numbers, complex numbers may be equal, as in the example: a + bi = c + di, where a and c and b and d must be equal.

Ex.
Find the values of x and y in 3x + yi = 5x + 1 + 2i

Solution: From the above definition for complex numbers equality, group the real numbers equal and do the same for the complex numbers to get the answer.

3x = 5x + 1          yi = 2i
-2x = 1                 y = 2
X = -(1/2)

Both examples show how to approach complex numbers problems.

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