What is one criterion to determine how resources are used?

A complex equation is an equation that involves complex numbers when solving it. A complex number is a number that has both a real part and an imaginary part. It is written in this form:

In the above equation, a and b both stand for numbers. For example, <4+3i> is a complex number. The 4 or a part is the real part of the number and the 3i or b part is the imaginary part of the number. Yes, the i stands for imaginary.

Imaginary Numbers

This i actually stands for the square root of -1. By squaring it, we will get -1. Don't worry about deriving these formulas; just know that i squared equals -1 and that i equals the square root of -1. That will help you out a lot!

Multiplying Complex Numbers

Let's see how the i part works itself out when we want to solve a complex equation that requires us to multiply two complex numbers together.

We start our multiplication the same way we would if we were multiplying two binomials together. We start by multiplying the 4 with each term in the second set of parentheses, and then, we add it to the 3i multiplied with each term in the second set of parentheses. When we multiply two i's together, we will treat it like we do a variable.

When we do end up multiplying two i's together, we get i squared, which we now know equals -1. We can replace our i squared with the -1, which gives us:

8 + 26i + (15 * -1) = 8 + 26i - 15

We then simplify our answer to:

x = -7 + 26i

Negative Square Roots

Now, this is only an example on how to solve the equation follow the steps you should get your answer.:)

Explanation: