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The argument of {(1 - i 3)}{(1 + i 3)} is

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The argument of $\frac{( 1 - i 3 )}{( 1 + i 3 )}$ is

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Text solutionVerified

z = \frac{1 - i 3}{1 + i 3} = \frac{( 1 - i 3 )}{( 1 + i 3 )} \times \frac{( 1 - i 3 )}{( 1 - i 3 )}

= \frac{1 + 3 i ^{2} - 2 3 i}{1 - 3 i ^{2}} = \frac{1 - 3 - 2 3 i}{1 + 3}

[∵ i^{2} = - 1]

= \frac{- 1 - i 3}{2} = - \frac{1}{2} - \frac{3}{2} i

∵ t an θ = \frac{3 /2}{1/2} = 3 [∵ t an θ = \frac{y}{x}]

∴

Argument of

z = θ = tan^{- 1} (3) = \frac{π}{3}

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