First slide

Algebra of complex numbers

Question

The product of the four values of ${(\frac{1}{2} + i \frac{\sqrt{3}}{2})}^{3 / 4}$ is

Moderate

A

-1
B

1
C

i
D

-i

Solution

$L e t x = {(\frac{1 + i \sqrt{3}}{2})}^{\frac{3}{4}} = {({(- w^{2})}^{3})}^{\frac{1}{4}} = {(- 1)}^{\frac{1}{4}} x^{4} + 1 = 0$
product of roots = 1

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