Question

find the sq root of 7+24i

Answer 1

root 7+24i = a+ib
squaring both sides
7+24i= (a+ib)squre
7+24i=a sqr-b sqr+2abi
7=a sqr-b sqr
24=2 ab
(a sqr +b sqr) =(a sqr-b sqr) ka whole sqr+4 a sqr b sqr
=7 sqr+(2ab )sqr
= 49+576
= 625
(a sqr + b sqr)ka whole sqr=625
a sqr + b sqr= 25
a sqr+ b sqr=25
a sqr - b sqr=7
compare both equations
a=4
b=3
root 7+24i = (4+3i)

Answer 2

$\sqrt{7 + 24i } = 4 + 3i$