Find the complex number w, lying in the first quadrant, and having the largest possible real part, which satisfies the equation:
w^6=-6-6*I*sqrt(3)
write your answer for w in polar form
Can u please help me with this question? the answer is 12^(1/6)*exp(2/9*I*Pi)
Thanks!
Did you mean to write above? If so you want the 6-th root
of with the
largest real part , so using de Moivre's formula we get:
.
Now just write down each root above and check which one has the largest real part. For example,
,
, etc.
Hint: Of course, you should check only those roots with angle in (why?)
Tonio