The value of - 1 + i 3 1 - i 30 is :

- 1 + 3 i 1 - i 30 = 2 cos 2 π 3 + i sin 2 π 3 2 cos π 4 - i sin π 4 30 = 2 30 ( cos 20 π + i sin 20 π ) 2 15 cos 15 π 2 - i sin 15 π 2 = 2 15 ( 1 + 0 i ) ( 0 + i ) = - 2 15 i

Home

Mathematics - Complex Number Question with Solution | TestHub

MathematicsComplex NumberCube Root of UnityEasy2 minPYQ_2020

MathematicsEasysingle choice

The value of ${(\frac{- 1 + i \sqrt{3}}{1 - i})}^{30}$ is :

Options:

Answer:

Solution:

${(\frac{- 1 + \sqrt{3} i}{1 - i})}^{30} = {(\frac{2 \cos (\frac{2 π}{3}) + i \sin (\frac{2 π}{3})}{\sqrt{2} (\cos \frac{π}{4} - i \sin \frac{π}{4})})}^{30}$

$= \frac{2^{30} (\cos 20 π + i \sin 20 π)}{2^{15} (\cos \frac{15 π}{2} - i \sin \frac{15 π}{2})}$

$= \frac{2^{15} (1 + 0 i)}{(0 + i)} = - 2^{15} i$

Stream:JEESubject:MathematicsTopic:Complex NumberSubtopic:Cube Root of Unity

⏱ 2mℹ️ Source: PYQ_2020

Doubts & Discussion

Loading discussions...