Question

find the square root of complex number 11+15i

Answer 1

Let x+yi is square root of 11+15i
SQUARING BOTH SIDE
(x+yi )^2 = 11+15i
x^2 -y^2 +2xi = 11+15i
so x^2 - y^2 = 11
2xy = 15
(x^2 + y^2 ) ^2 = (x^2 - y^2) ^2 + (2xy)^2
(x^2+y^2)^2 = 11^2 + 15^2
(x^2 + y^2)^2 = 346
x^2 + y ^2 = 18.6
x^2 - y ^2 = 11 (given)
2x^2 = 29.6
x = +/- 3.8
x^2 + y^2 =18.6
14.8 + y^2 = 18.6
y^2 = 3.8
y = + / - 1.9
2xy = 15 so x and y are both positive as well as both negative
so square root of 11 + 15i = +/- 3.8 +/- 1.9 i


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