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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.

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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, 
\[z = \sqrt{2}\left( 1 + i \right)\].
  Is there an error in this question or solution?
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APPEARS IN

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