Algebra 2 Common Core

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

Chapter 4 - Quadratic Functions and Equations - Chapter Test - Page 273: 7

Answer

$-2 + 12i$

Work Step by Step

Use the definition of the square roots of negative numbers: $4\sqrt {-9} - 2 = 4\sqrt {(-1)(9)} - 2$ Use the multiplication property of square roots to rewrite the radical: $4\sqrt {(-1)(9)} - 2 = \sqrt {-1} \cdot \sqrt {9} - 2$ Use the definition of $i$ to substitute for $\sqrt {-1}$: $4 \cdot i \cdot \sqrt {9} - 2$ Take the square root of $9$: $4 \cdot i \cdot 3 - 2$ Multiply to simplify: $12i - 2$ Rewrite the solution in a more conventional way with the imaginary number placed last: $-2 + 12i$
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