First slide

Algebra of complex numbers

Question

If $z = \sqrt{20 i - 21} + \sqrt{20 i + 21,}$ than one of the possible value of $| a r g (z) |$ equals

Moderate

A

$π / 4$
B

$π / 2$
C

$3 π / 8$
D

$π$

Solution

$20 i + 21 = {(5 + 2 i)}^{2}$ and $20 i + 21 = {(2 - 5 i)}^{2}$
$∴ z = \pm (5 + 2 i) \pm (2 + 5 i) \Rightarrow z = 7 (1 + i), 3 (1 - i), 3 (- 1 + i), (- 1 - i) \Rightarrow a r g (z) = π / 4, - π / 4, 3 π / 4, - 3 π / 4$
Thus, one of the possible value of $| a r g (z) |$ is $π / 4 .$

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