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Trigonometry

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Moderate

Complex Number, Trigonometric Form, Quadrant II, Exact Value

TRIG-N5@FF7

Write the complex number $ z=-2+2i$ in trigonometric form.

A

$ z=2\sqrt { 2 }\left( \cos { \left( -\cfrac { 3\pi }{ 4 } \right) +i } \sin { \left( -\cfrac { 3\pi }{ 4 } \right) } \right)$

B

$ z=2\sqrt { 2 }\left( \cos { \left( \cfrac { 3\pi }{ 4 } \right) +i } \sin { \left( \cfrac { 3\pi }{ 4 } \right) } \right)$

C

$ z=2\sqrt { 2 }\left( \cos { \left( -\cfrac { 3\pi }{ 2 } \right) +i } \sin { \left( -\cfrac { 3\pi }{ 2 } \right) } \right)$

D

$ z=2\sqrt { 2 }\left( \cos { \left( \cfrac { 3\pi }{ 2 } \right) +i } \sin { \left( \cfrac { 3\pi }{ 2 } \right) } \right)$