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Question Number 33463 by NECx last updated on 17/Apr/18

$$Findthepricipalandordinary$$$$argumentofz=\frac{i}{-2-2i}$$

Commented by abdo imad last updated on 17/Apr/18

$$z=\frac{-i}{2(1+i)}=\frac{-i(1-i)}{4}=\frac{1-i}{4}\Rightarrow \mid z\mid =\frac{1}{4}\mid 1-i\mid =\frac{\sqrt{2}}{4}$$$$z=\frac{1}{4}-\frac{i}{4}=\frac{\sqrt{2}}{4}(\frac{1}{\sqrt{2}}-\frac{i}{\sqrt{2}})=\frac{\sqrt{2}}{2}{e}^{-i\frac{\pi }{4}}\Rightarrow arg\left(z\right)\equiv -\frac{\pi }{4}\left[2\pi \right].$$

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