Q. 143.8( 12 Votes )

Write (i25)3 in polar form.

Answer :

Given Complex number is Z = (i25)3


Z = i75


Z = i74.i


Z = (i2)37.i


We know that i2 = - 1


Z = ( - 1)37.i


Z = ( - 1).i


Z = - i


Z = 0 - i


We know that the polar form of a complex number Z = x + iy is given by Z = |Z|(cosθ + isinθ)


Where,


|Z| = modulus of complex number =


θ = arg(z) = argument of complex number =


Now for the given problem,





|z| = 1



Since x>0,y<0 complex number lies in 4th quadrant and the value of θ will be as follows - 900≤θ≤00.



.




The Polar form of Z = (i25)3 is .


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