If z is a complex number such that | z | = 4 and arg ,(z) = frac {5π }{6} , then z is equal to

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4-1.Complex numbers

normal

If $z$ is a complex number such that $| z | = 4$ and $arg \,(z) = \frac {5\pi }{6}$ , then $z$ is equal to

A

$ - 2\sqrt 3 + 2i$

B

$2\sqrt 3 + i$

C

$2\sqrt 3 - 2i$

D

$ - \sqrt 3 + i$

Solution

$r=4, \theta=5 \frac{\pi}{6}$

$z=x+i y=r(\cos \theta+i \sin \theta)$

hence

$z=-2 \sqrt{3}+2 i$

Standard 11

Mathematics

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