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=-1+i.

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=-1+i .

Answer

r=-\sqrt{2}  and   	heta = \dfrac{3\pi}{4}  hence   z=-\sqrt{2}	ext{cis}\left(\dfrac{3\pi}{4}ight)=-\sqrt{2}e^{\frac{3\pi}{4}i} .

Answer

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

Answer

r=\sqrt{2}  and   	heta = \dfrac{3\pi}{4}  hence   z=\sqrt{2}	ext{cis}\left(\dfrac{3\pi}{4}ight)=\sqrt{2}e^{\frac{3\pi}{4}i} .

Answer

r=2  and   	heta = \dfrac{3\pi}{4}  hence   z=2	ext{cis}\left(\dfrac{3\pi}{4}ight)=2e^{\frac{3\pi}{4}i} .

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

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