Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSComplex Numbers and Quadratic Equations2 Marks
Question
Find principal argument of $(1+\text{i}\sqrt{3})^2$
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Answer
We have, $\text{z}=(1+\text{i}\sqrt{3})^2$ $\Rightarrow\text{z}=1-3+2\text{i}\sqrt{3}$ $\Rightarrow\text{z}=-2+\text{i}(2\sqrt{3})$ So, z lies in second quadrant. $\Rightarrow\arg(\text{z})=\pi-\tan^{-1}\Big|\frac{2\sqrt{3}}{-2}\Big|$ $\Rightarrow\arg(\text{z})=\pi-\tan^{-1}\sqrt{3}$ $\Rightarrow\arg(\text{z})=\pi-\frac{\pi}{3}$ $\Rightarrow\arg(\text{z})=\frac{2\pi}{3}$
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