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in Complex Numbers by (29.6k points)
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Write (i25)3 in polar form.

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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= \(\sqrt{x^2+y^2}\)

θ =arg(z)=argument of complex number= tan-1\(\Big(\frac{|y|}{|x|}\Big)\)

Now for the given problem,

Since x>0,y<0 complex number lies in 4th quadrant and the value of θ will be as follows -90 °≤θ≤0°.

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