Question

Use de moivre's theorem to write the complex number in trigonometric form. ((sqrt3)+i)^3

Answer 1

Note that sqrt( sqrt(3)^2 + 1^2 ) 
= sqrt( 3 + 1 ) 
= 2 

The (√3+i) = 2 * (√3/2+i/2) 
= 2 * ( cos(pi/6) + i * sin(pi/6)) 

So that (√3+i)^3 = ( 2 * ( cos(pi/6) + i * sin(pi/6)) ) ^ 3 
= 8 * ( cos(pi/6) + i * sin(pi/6)) ^ 3 
= 8 * ( cos(3*pi/6) + i * sin(3* pi/6)) 

= 8 * ( cos(pi/2) + i * sin(pi/2) 

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