Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.6 - Complex Numbers - 1.6 Exercises - Page 64: 56


$\sqrt \frac{1}{3}\sqrt -27=3i$

Work Step by Step

Since $i=\sqrt -1$ we can write $\sqrt \frac{1}{3}\times\sqrt -27=\sqrt \frac{1}{3}\times i\sqrt 27$. We can write $i\sqrt 27=i\sqrt (3\times9)=3i\sqrt 3$ hence $\sqrt \frac{1}{3}\times i\sqrt 27=\sqrt \frac{1}{3}\times3i\sqrt 3=\frac{1}{\sqrt 3}\times3i\sqrt 3 =\frac{3i\sqrt 3}{\sqrt 3}$. The $\sqrt 3$'s then cancel each other which leaves a final answer of $3i$. Hence the final answer written in the form $a+bi$ where $a$ is the real part and $b$ is the imaginary part is $3i$ as $a=0$ and $b=3$.
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