Question

Find the square root of the following complex numbers:_ (1) 3 – 4i
(2) –3 + 4i
(3) 7 – 24i
4) –21 + 20i
5) –5 – 12i​

Answer 1

$\huge\bf\underline\bold\red{AnSwEr}$

Pls refer to the attached pic.

Answer 2

± (2 + i)

Let 3+4i=x+iy

Then (3+4i)2=(x+iy)2⇒3+4i=x−y+2ixy

Comparing real part and imaginary part, we get

3=x−y and 2xy=4⇒xy=4

∴x+y=±5     ( As x=−5;x is real part )

∴x=4,y=1⇒x=±2,y=±1

Hence square root is ±(2+i)