First slide

Algebra of complex numbers

Question

$x = 3, y = ω^{2} + 2 ω, z = ω + 2 ω^{2}$ then $x^{2} + y^{2} + z^{2} =$

Easy

A

12
B

24
C

36
D

48

Solution

$x^{2} + y^{2} + z^{2} =$ $9 + {(ω^{2} + 2 ω)}^{2} + {(ω + 2 ω^{2})}^{2}$
$= 9 + ω^{4} + 4 ω^{2} + 4 ω^{3} + ω^{2} + 4 ω^{4} + 4 ω^{3}$

$= 9 + 4 + 4 + 5 ω^{4} + 5 ω^{2}$

$= 9 + 8 - 5 = 12$

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