Find the square root of the following complex number: `-11-60sqrt(-1)`

Explanation

`-11 – 60sqrt(-1)`

Given `-11 – 60sqrt(-1)`

`z = -11 – 60sqrt(-1)`
Therefore, `sqrt(a + ib) = -11 – 60sqrt(-1) = -11 – 60i`

Here, `b < 0`

`sqrt(-11-60i)=+-[(frac{-11+sqrt((-11)^2+(-60)^2)}{2})^frac{1}{2}-i(frac{-11+sqrt((-11)^2+(-60)^2)}{2})^frac{1}{2}]`

`=+-[(frac{-11+sqrt(121+3600)}{2})^frac{1}{2}-i(frac{11+sqrt(121+3600)}{2})^frac{1}{2}]`

`=+-[(frac{-11+sqrt(3721)}{2})^frac{1}{2}-i(frac{11+sqrt(3721)}{2})^frac{1}{2}]`

`=+-[(frac{-11+61}{2})^frac{1}{2}-i(frac{11+61}{2})^frac{1}{2}]`
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