A complex number can be written in exponential form as $z=re^{i\theta}$ z=re^{i\theta} where $r\geq0$ r\geq0 and $\theta \in R$ \theta \in R is in radians.
Choose the correct response for the complex number z=2i.

Question

A complex number can be written in exponential form as   z=re^{i	heta}  where   r\geq0  and   	heta \in R  is in radians.  Choose the correct response for the complex number   z=2i .

Answer

r=4  and   	heta = \dfrac{\pi}{2}  hence   z=4	ext{cis}\left(\dfrac{\pi}{2}ight)=4e^{\frac{\pi}{2}i} .

Answer

r=2  and   	heta = \pi  hence   z=2	ext{cis}\left(\piight)=2e^{\pi i} .

Answer

r=2  and   	heta = \dfrac{\pi}{2}  hence   z=2	ext{cis}\left(\dfrac{\pi}{2}ight)=2e^{\frac{\pi}{2}i} .

Answer

r=\sqrt{2}  and   	heta = \dfrac{\pi}{2}  hence   z=\sqrt{2}	ext{cis}\left(\dfrac{\pi}{2}ight)=\sqrt{2}e^{\frac{\pi}{2}i} .

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A complex number can be written in exponential form as z=re^{i\theta} where ...

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