Write (i25)3 in polar form.

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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RS Aggarwal - Mathematics