First slide

Algebra of complex numbers

Question

If $ω \neq 1$ is a cube root of unity and $(1 + ω)^{2017} =$ $A + B (ω)$ Then A and B are respectively the numbers

Easy

A

0 ,1
B

1 ,1
C

1 ,0
D

-1 , 1

Solution

$(1 + ω)^{2017} = {(- ω^{2})}^{2017} = - ω^{4034} = - ω^{2}$
$∴ A + B ω = 1 + ω \Rightarrow A = 1, B = 1$

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