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

InterviewSolution

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

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