Q:
# How do you simplify imaginary numbers?

Imaginary numbers are typically simplified in the same way that expressions with the variable x are simplified, with the exception of the expression i^2, which has a value equal to -1. For example, the expression 2i + 8i can be simplified by writing it first as (2 + 8) * i, with the final expression written as 10i.

Continue Reading
Credit:
khoa vu
Moment
Getty Images

For division problems, imaginary numbers are simplified by clearing the denominator by multiplying the expression by the conjugate of the denominator over itself, which is the same as multiplying by one and does not change the value of the expression. For example, in the problem (2 + i)/(3 + 4i) is simplified by multiplying it by (3 - 4i)/(3 - 4i), which results in the simplified fraction (10 - i)/25.

Any time i is taken to an odd exponent, it is equal to either i or -i. When taken to an even exponent, i is always equal to -1. When i is expressed to the power of zero, it is equal to 1. In the problem 4i * 5i, the simplified form comes from rewriting the expression as (4 * 5)(i^2). Since 4 * 5 is equal to 20 and i^2 is equal to -1, the final solution for the problem is -12.

Learn more about Algebra-
Q:
## What do brackets mean in math?

A: In math, brackets are used to group numbers and expressions together and to represent multiplication in expressions that already contain parenthesis. If ex... Full Answer >Filed Under: -
Q:
## How are equations factored in algebra?

A: Factoring in algebra involves finding the factors of numbers and expressions by simplifying the equation. The process may be more complex depending on the ... Full Answer >Filed Under: -
Q:
## How do you divide integers?

A: Divide integers the same way you do with whole numbers. Divide the absolute values, and then determine the sign of the answer based on the signs of the int... Full Answer >Filed Under: -
Q:
## How are imaginary denominators rationalized?

A: To rationalize an imaginary denominator, multiply both the numerator and denominator by the complex conjugate of the denominator. Multiply out the terms in... Full Answer >Filed Under: