Question

Which expression is a fourth root of (-1 + iSqrt3)

A.4sqrt2(cos(280)+ isin(280))
B. 4sqrt2(cos(30)+ isin(30))
C.4sqrt2(cos(60)+ isin(60))
D.4sqrt2(cos(320)+ isin(320))

Answer 1

\[(-1+ i \sqrt3) \]

Answer 2

find
\(\theta = \tan^{-1} (-\sqrt 3) = ...\)

Answer 3

-60

Answer 4

so should i be getting \[\sqrt[4]{2}(\cos(60) + isin(60)\]

Answer 5

that was wrong but thats okay XD

Answer 6

sorry for the late reply.
since (-1 + iSqrt3) is in 2nd quadrant,
theta will be 120 degrees

so we have r<theta = 2 <120

taking 4th root of complex number means taking 4th root of 'r' and dividing the angle theta by 4

so, 4th root will be
\(\sqrt[4]2 \angle 120/4 = \sqrt [4]2 \angle 30 =\sqrt [4]2(\cos 30 +i \sin 30) \)

Answer 7

no problem :) thank you again, your help is very Super Saiyan worthy!

Answer 8

welcome ^_^
i'll take the compliment, thanks ;)