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Find the square root for (-5+12i)...

Find the square root for `(-5+12i)`

Text Solution

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We solve `sqrt(a+ib)=`
`=[sqrt((sqrt(a^(2)+b^(2)+a))/(2))+isqrt((sqrt(a^(2)+b^(2)-a))/(2))]`
In this examle `a=-5, b=12`
Hence
`+-[ sqrt(sqrt(25+144+(-5))/(2))+sqrt(sqrt(25+144-(-5))/(2))]`
`=+-[sqrt((13-5)/(2))+sqrt((13+5)/(2))]`
`=+-(2+3i)`
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