The roots of 2-2 i1-3A- 1-2 i-1-i-2-2 iB- None of the aboveC- -2cos-12-i sin-12 -2-sin-12-i cos-12-1-iD- -2cos-12-i sin-12 -2-sin-12-i cos-12- 1-i

The correct option is C Using De Moivre's theoram (cosθ+isinθ)^n=(cosnθ+isinnθ) nbsp; And putting n=0,1,2 then we get required roots. ...

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Trigonometric Ratios of Multiples of an Angle

The roots of ...

Question

The roots of $(2 - 2 i)^{\frac{1}{3}}$

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None of the above

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Solution

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$\frac{1 - i}{1 + i}$ is equal to

z_{1} = 1 - i

z_{2} = \sqrt{3} + i

z_{1} \cdot z_{2}

i + \sqrt{3}

{⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \frac{1 + cos (\frac{π}{12}) + i sin (\frac{π}{12})}{1 + cos (\frac{π}{12}) - i sin (\frac{π}{12})} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦}^{72} =

cos \frac{π}{12} - sin \frac{π}{12} = \frac{1}{\sqrt{2}}

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