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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

Text Solution

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`z= |z|(e^(img(z)))`
`= 4(e^(i5 pi/6))`
`= 4(cos 5 pi/6 + i sin 5 pi/6)`
`= 4[cos(pi-pi/6) + i sin( pi - pi/6)]`
`= 4[- sqrt3/2 + i 1/2]`
`= 2[- sqrt3 + i]`
`z = - 2 sqrt 3 + 2i`
option 1 is correct
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