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Complex Numbers — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSComplex Numbers2 Marks
Question
Find the modulus and argument of the following complex numbers and hence express each of them in the polar form: $1-\text{i}$
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Answer

Modulus, $|1-\text{i}|=\sqrt{1^2+1^2}=\sqrt{2}$ Argument, $\text{arg}(1-\text{i})=\tan^{-1}\Big(\frac{-1}{1}\Big)=\tan^{-1}(-1)=-\frac{\pi}{4}$ Polar form, $\sqrt{2}\Big(\cos\frac{\pi}{4}-\text{i}\sin\frac{\pi}{4}\Big)$

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