Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 6 - Section 6.4 - Graphs of Polar Equations - Exercise Set - Page 755: 100


The result in the standard form is $8$.

Work Step by Step

Perform the standard operation and expand the given expression as below: $\left( -1+i\sqrt{3} \right)\left( -1+i\sqrt{3} \right)\left( -1+i\sqrt{3} \right)$. $\begin{align} & =\,\left( -1+i\sqrt{3} \right)\left( 1-i\sqrt{3}-i\sqrt{3}+3{{i}^{2}} \right) \\ & =\left( -1+i\sqrt{3} \right)\left( 1-2i\sqrt{3}+3{{i}^{2}} \right) \\ & =\left( -1+i\sqrt{3} \right)\left( 1-2i\sqrt{3}-3 \right) \\ & =\left( -1+i\sqrt{3} \right)\left( -2-2i\sqrt{3} \right) \end{align}$ Now, perform the multiplication operation again on the above reduced equation and simplify it as below: $\begin{align} & =\left( -1+i\sqrt{3} \right)\left( -2-2i\sqrt{3} \right) \\ & =\left( 2+2i\sqrt{3}-2i\sqrt{3}-6{{i}^{2}} \right) \\ & =2+6 \\ & =8 \\ \end{align}$ Therefore, the result in the standard form is $8$.
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