Question

Find the square root of 3+4i

Answer 1

let x + iy be square root of (3 - 4i)

(x + iy)2 = 3 - 4i

x2 - y2 + 2xyi = 3 - 4i

on comparing

x2 - y2 = 3  -----(1)

2xy = -4

we have

(x2 + y2)2 = (x2 - y2)2 + (2xy)2

(x2 + y2)2 = 9 + 16

x2 + y2 = 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)

Answer 2

=> ✓3+✓4
=> ✓3 +2

This is your answer