Question

the polar form of (i^25)^3 is​

Answer 1

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