Find the square root of 7-24i
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Q)Find the square root of 7-24i :
Ans:-) (a+bi)(a+bi)=7-24i
a^2-b^2+2abi=7-24i
The real parts are equal, as are the real coefficients of the imaginary parts:
a^2-b^2=7
2abi=-24i
ab=-12==>a=-12/b Substituting we get:
(-12/b)^2-b^2=7
144/b^2-b^2=7
b^4+7b^2-144=0
(b^2+16)(b^2-9)=0
Since b is real b=3 or -3
a^2-9=7 ==> a^2=16 ==> a=+-4
Since ab=-12 one of a or b is negative.
So either of z=4-3i or z=-4+3i is a square root of 7-24i
(4-3i)(4-3i)=16-24i+9i^2=7-24i
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