1

0

let x + iy be square root of (3 - 4i)

(x + iy)^{2} = 3 - 4i

x^{2 }- y^{2} + 2xyi = 3 - 4i

on comparing

x^{2} - y^{2} = 3 -----(1)

2xy = -4

we have

(x^{2} + y^{2})^{2} = (x^{2} - y^{2})^{2} + (2xy)^{2}

(x^{2 }+ y^{2})^{2} = 9 + 16

x^{2} + y^{2} = 5 ------(2)

from (1) and (2)

x = +- 2

y = +-1

Check by putting which combination satisfies.

Square root of (3 - 4i) is (+-2 -+i)

ie, (2 - i) and (-2 + i)