Express $1 - i$ in the modulus-amplitude form

\sqrt{2} (c o s (- π / 4) + i s i n (- π / 4))

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(c o s (- π / 4) + i s i n (- π / 4))

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\sqrt{2} (c o s (- π / 4) - i s i n (- π / 4))

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(c o s (- π / 4) - i s i n (- π / 4))

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Solution

The correct option is A $\sqrt{2} (c o s (- π / 4) + i s i n (- π / 4))$
Multiplying and dividing by $\sqrt{2}$ we get
$\sqrt{2} (\frac{1 - i}{\sqrt{2}})$
$= \sqrt{2} (\frac{1}{\sqrt{2}} - \frac{i}{\sqrt{2}})$
$= \sqrt{2} (c o s 45^{0} - i s i n 45^{0})$
$= \sqrt{2} (c o s (- 45^{0}) + i s i n (- 45^{0}))$

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