Put the complex number `(1+7i)/((2-i)^2)` in the form `r(costheta+i\ sintheta)`, where `r` is a positive real number and `-pilttheta le pi`.

Explanation

`(1+7i)/(2−i) ^2=(1+7i)/((2−i) ^2) xx (2+i)^2/(2+i) ^2'


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`=frac{-25+25i}{(2^2+1)^2}`
`=-1+i`

Here `r cos theta=-1` and `r sin theta=1`

`r^2(cos^2 theta+sin^2 theta)=2=>r=sqrt2`

`sqrt2 cos theta=-1` and `sqrt2 sin thet=1`

`cos theta= frac{-1}{sqrt2}` and `sin theta=frac{1}{sqrt2}`
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