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Question

USE DeMoivre's THEOREM TO FIND [2(cos pie/6 + i sin pie/6)]^5. state the result in standard complex number form. determine the absolute value of the complex number and the quadrant in which the corresponding point lies.

Answer 1

in polar form
z=2(cospi/6 +i sinpi/6)= 2< pi/6
so
z^5= 2^5 (cos5pi/6+i sin 5pi/6) = 32( -sqrt3 /2 +1/2 i)=

-16sqrt3 +16 i (in the second quadrant as the real part is <0 and the imaginary part>0)
The modulus is 32