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If z is a complex number such that |z|=4...

If z is a complex number such that `|z|=4` and `arg(z) =(5pi)/6` then z is equal to

A

` 2sqrt3+2i`

B

`2sqrt3-2i`

C

`-2sqrt3+2i`

D

`-sqrt3+i`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `z=K(costheta+isintheta)`
`|z|=sqrt(K^(2)(cos^(2)theta+sin^(2)theta))=4`
`thereforeK=4`
Again Arg `(z)=(5pi)/(6)`
So, `theta=(5pi)/(6)`
Now, `x=4(cos((5pi)/(6))+isin((5pi)/(6)))`
`=4((-sqrt3)/(2)+i((1))/(2))=-2sqrt3+2i`
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