Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSComplex Numbers and Quadratic Equations2 Marks
Question
Find z if |z| = 4 and $\arg(\text{z})=\frac{5\pi}{6}$
✓
Answer
Let $\text{z}=|\text{z}|(cos\theta+\text{i}\sin\theta),$ where $\theta=\arg(\text{z})$ Given that, |z| = 4 and$\arg(\text{z})=\frac{5\pi}{6}$ $\Rightarrow\text{z}=4\Big[\cos\frac{5\pi}{6}+\text{i}\sin\frac{5\pi}{6}\Big]$ (z lies in II quadrant) $\Rightarrow\text{z}=4\Big[-\frac{\sqrt{3}}{2}+\text{i}\frac{1}{2}\Big]$ $\Rightarrow\text{z}=-2\sqrt{3}+2\text{i}$
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