Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 4 - Quadratic Functions and Equations - 4-8 Complex Numbers - Practice and Problem-Solving Exercises - Page 253: 26

Answer

$65+72i$

Work Step by Step

Using $(a+b)^2=a^2+2ab+b^2$ or the square of a binomial, the given expression, $ (9+4i)^2 ,$ is equivalent to \begin{align*} & (9)^2+2(9)(4i)+(4i)^2 \\&= 81+72i+16i^2 \\&= 81+72i+16(-1) &\text{ (use $i^2=-1$)} \\&= 81+72i-16 .\end{align*} Combining the real parts, the expression above is equivalent to \begin{align*} & (81-16)+72i \\&= 65+72i .\end{align*} Hence, the simplified form of the given expression is $ 65+72i $.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.