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Find Z, If | Z | = 4 and Arg ( Z ) = 5 π 6 . - Mathematics

Find z, if \[\left| z \right| = 4 \text { and }\arg(z) = \frac{5\pi}{6} .\]

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Solution

We know that,

\[z = \left| z \right|\left\{ \cos\left[ \arg(z) \right] + i\sin\left[ \arg(z) \right] \right\}\]

\[ \Rightarrow z = 4\left( \cos\frac{5\pi}{6} + i\sin\frac{5\pi}{6} \right)\]

\[ = 4\left( - \cos\frac{\pi}{6} + i\sin\frac{\pi}{6} \right)\]

\[ = 4\left( - \frac{\sqrt{3}}{2} + \frac{1}{2}i \right)\]

\[ = - 2\sqrt{3} + 2i\]

Thus, 

\[z = - 2\sqrt{3} + 2i\]

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 13 Complex Numbers
Q 12 | Page 62
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