Find the modulus and argument of the following complex numbers and hence express each of them in the polar form: 1 - i

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Solution

$1 - i = \sqrt{2} (\frac{1}{\sqrt{2}} - \frac{i}{\sqrt{2}}) = \sqrt{2} (cos \frac{7 π}{4} + i sin \frac{7 π}{4}) = \sqrt{2} e^{i \frac{7 π}{4}}$
Modulus and argument of $1 - i$ is $\sqrt{2}$ and $\frac{7 π}{4}$ respectively

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Find the modulus and argument of the following complex numbers and hence express each of them in the polar form: 1 - i

1−i=√2(1√2−i√2)=√2(cos7π4+isin7π4)=√2ei7π4Modulus and argument of 1−i is √2 and 7π4 respectively

$1 - i = \sqrt{2} (\frac{1}{\sqrt{2}} - \frac{i}{\sqrt{2}}) = \sqrt{2} (cos \frac{7 π}{4} + i sin \frac{7 π}{4}) = \sqrt{2} e^{i \frac{7 π}{4}}$
Modulus and argument of $1 - i$ is $\sqrt{2}$ and $\frac{7 π}{4}$ respectively