Write $(1 - i)$ in polar form.

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Solution

Given,

$z = 1 - i$

$z = a + i b$

$r = \sqrt{a^{2} + b^{2}} = \sqrt{1^{2} + (- 1)^{2}} = \sqrt{2}$

$θ = tan - 1 \frac{b}{a} = tan - 1 \frac{- 1}{1} = - \frac{π}{4}$

$\Rightarrow θ = π - \frac{π}{4} = \frac{3 π}{4}$

$z = r (cos θ + i sin θ)$

$z = \sqrt{2} (cos \frac{3 π}{4} + i sin \frac{3 π}{4})$

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