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 - Lesson Check - Page 253: 5



Work Step by Step

Using $(a+b)(c+d)=ac+ad+bc+bd$ or the FOIL Method, the given expression, $ (2+i)(4-5i) ,$ is equivalent to \begin{align*} & 2(4)+2(-5i)+i(4)+i(-5i) \\&= 8-10i+4i-5i^2 \\&= 8-10i+4i-5(-1) &\text{ (use $i^2=-1$)} \\&= 8-10i+4i+5 .\end{align*} Combining the real parts and the imaginary parts, the expression above is equivalent to \begin{align*} & (8+5)+(-10i+4i) \\&= 13+(-6i) \\&= 13-6i .\end{align*} Hence, the simplified form of the given expression is $ 13-6i $.
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