Thread: Complex numbers in polar

Hi All,
I am preparing for my BCA 2nd semester examination.I came across with a mathematical question in which i am stuck please help.

Find all the sixth roots of (12 + 5i)







Thanks
Arun.

Originally Posted by arunkayal

Hi All,
I am preparing for my BCA 2nd semester examination.I came across with a mathematical question in which i am stuck please help.

Find all the sixth roots of (12 + 5i)

Convert to polar representation@

(12 + 5i) = sqrt(12^2 + 5^2) exp(i*[arctan(5/12)+2*n*pi]), n= 0, +/-1, ...

Then

(12 + 5i)^(1/6) = (12^2 + 5^2)^(1/12) exp(i*[arctan(5/12)+2*n*pi]/6), n= 0, +/-1, ...

of which only 6 are distinct, say n = 0. 1, 2, ..5.

RonL