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: 55


$\sqrt -3\times\sqrt -12=-6$

Work Step by Step

Since $i=\sqrt -1$ we can write $\sqrt -3\times\sqrt -12=i\sqrt 3\times i\sqrt 12$. We can write $i\sqrt 12=2i\sqrt 3$ hence $i\sqrt 3\times i\sqrt 12=i\sqrt 3\times2i\sqrt 3=2i^{2}(\sqrt 3\times\sqrt 3)=2i^{2}\times3=6i^2$ however we know that $i^{2}=-1$ hence $6i^{2}=-6$. Hence the final answer written in the form $a+bi$ where $a$ is the real part and $b$ is the imaginary part is $-6$ as $a=-6$ and $b=0$.
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