# If | Z | = 2 and Arg ( Z ) = π 4 ,Find Z. - Mathematics

If $\left| z \right| = 2 \text { and } \arg\left( z \right) = \frac{\pi}{4}$,find z.

#### Solution

We know that,

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

$= 2\left( \cos\frac{\pi}{4} + i\sin\frac{\pi}{4} \right)$

$= 2\left( \frac{1}{\sqrt{2}} + i\frac{1}{\sqrt{2}} \right)$

$= \sqrt{2}\left( 1 + i \right)$
Hence,
$z = \sqrt{2}\left( 1 + i \right)$.
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 13 Complex Numbers
Q 23 | Page 63