Complex Numbers

Aladdin

Full Member
Joined
Mar 27, 2009
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553
For what value of the natural number n is the complex number (1+i3)n\displaystyle ( 1 + i\sqrt{3} )^n real and positive ?
Real and negative ? Pure Imaginary ?

Thanks in advance .
 
Aladdin said:
For what value of the natural number n is the complex number (1+i3)n\displaystyle ( 1 + i\sqrt{3} )^n real and positive ?
Real and negative ? Pure Imaginary ?

Thanks in advance .

(1+i3)n=12nei(nπ3+2nkπ)\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!!!
 
Subhotosh Khan said:
Aladdin said:
For what value of the natural number n is the complex number (1+i3)n\displaystyle ( 1 + i\sqrt{3} )^n real and positive ?
Real and negative ? Pure Imaginary ?

Thanks in advance .

(1+i3)n=12nei(nπ3+2nkπ)\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
 
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