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 .