Trigonometry

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Converting Trig Form to Standard Form, Complex Numbers

TRIG-OH8VYB

Write the complex number in standard form:

$$z=8\left[ \cos { \left( \cfrac { 3\pi }{ 4 } \right) } +i\sin { \left( \cfrac { 3\pi }{ 4 } \right) } \right]$$

A

$z=-4\sqrt { 2 } +4i\sqrt { 2 }$

B

$z=-\cfrac { \sqrt { 2 } }{ 2 } +i\cfrac { \sqrt { 2 } }{ 2 }$

C

$z=-8\sqrt { 2 } +8i\sqrt { 2 }$

D

$z=4\sqrt { 2 } -i4\sqrt { 2 }$