Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.1 Complex Numbers - 8.1 Exercises: 16

Answer

complex, pure imaginary, non-real complex

Work Step by Step

$\sqrt (-36)=\sqrt (-1\times36)=\sqrt -1 \times \sqrt (36)=i\times6=6i$ If a and b are real numbers, then any number of the form $a+bi$ is a complex number. Since $a=0$ and $b=6$ and both $a$ and $b$ are real numbers, $6i$ is a complex number. Also, If $a=0$ and $b\ne0$, the complex number is said to be a pure imaginary number. Since $b=6$, $6i$ can be labelled as a pure imaginary number as well. Since pure imaginary numbers are a subset of non-real complex numbers, $6i$ can be labelled as a non-real complex number as well.
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