Complex Numbers

[Aladdin]

For what value of the natural number n is the complex number \(\displaystyle ( 1 + i\sqrt{3} )^n\) real and positive ?
Real and negative ? Pure Imaginary ?

Thanks in advance .

 

[Deleted member 4993]

For what value of the natural number n is the complex number \(\displaystyle ( 1 + i\sqrt{3} )^n\) real and positive ?
Real and negative ? Pure Imaginary ?

Thanks in advance .

\(\displaystyle (1+i\sqrt{3})^n = \frac{1}{2^n}e^{i(\frac{n\pi}{3}+2nk\pi)}\)

Aladdin _ you know the drill - where is your work!!!

 

[Aladdin]

For what value of the natural number n is the complex number \(\displaystyle ( 1 + i\sqrt{3} )^n\) real and positive ?
Real and negative ? Pure Imaginary ?

Thanks in advance .

\(\displaystyle (1+i\sqrt{3})^n = \frac{1}{2^n}e^{i(\frac{n\pi}{3}+2nk\pi)}\)

Aladdin _ you know the drill - where is your work!!!

Okitoo -- Thanks Mr Khan