CBSE BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers and Quadratic Equations1 Mark
Question
If z = 4 and $\arg(\text{z})=\frac{5\pi}{6},$ then z = __________.
✓
Answer
If z = 4 and $\arg(\text{z})=\frac{5\pi}{6},$ then z $=-2\sqrt{3}+2\text{i}$ Solution:
Let $\text{z}=|\text{z}|(\cos\theta+\text{i}\sin\theta)$
Where $\theta=\text{arg(z)}$
Given that |z| = 4 and $\text{arg(z)}=\frac{5\pi}{6}$
$\text{z}=4\Big[\cos\frac{5\pi}{6}+\text{i}\sin\frac{5\pi}{6}\Big]$ (z lies in II quadrant)
$=4\Big[-\frac{\sqrt{3}}{2}+\text{i}\frac{1}{2}\Big]$
$=-2\sqrt{3}+2\text{i}$
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