First slide

Algebra of complex numbers

Question

If $z = {(\frac{1}{\sqrt{3}} + \frac{1}{2} i)}^{7} + {(\frac{1}{\sqrt{3}} - \frac{1}{2} i)}^{7}$ then

Moderate

A

Re $(z) = 0$
B

$Im (z) = 0$
C

$Re (z) > 0, Im (z) < 0$
D

$Re (z) < 0, Im (z) > 0$

Solution

$\bar{z} = {(\frac{1}{\sqrt{3}} - \frac{1}{2} i)}^{7} + {(\frac{1}{\sqrt{3}} + \frac{1}{2} i)}^{7} = z$
$\Rightarrow z$ is purely real
$∴ Im (z) = 0$

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