Question

Find the squareroots of Z=5+12i

Answer 1

Answer:

Suppose that a+bi is a square root of 5 + 12i. Then, (a+bi)^2 = (a^2 - b^2) + (2ab)i = 5 + 12i

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

let square root of Z be x+iy

so,

(x+iy)^2=5+12i

x^2-y^2+2xyi=5+12i

COMPARING THE COEFFICIENTS:-

2xyi=12i

2xy=12

xy=6

y=6/x

x^2-y^2=5

x^2-(6/x)^2=5

x=3,-3

so y=2,-2

so if x=3,y=2

then square root is 3+2i

if x=-3 y=-2

then square root is -3-2i