Question

The square root of 3 - 4i is

• A. $\pm$(2+i).
• B. $\pm$(2-i).
• C. $\pm$(1-2i).
• D. $\pm$(1+2i).

Answer 1

The correct option is B

$\pm$(2-i).

Let $\sqrt{3-4i}$=x+iy $\Rightarrow$ 3-4i= $x^2$-$y^2$+2ixy

$\Rightarrow$ $x^2$-$y^2$=3, 2xy=-4 ..........(i)

$\Rightarrow$ ${(x^2+y^2)}^2$=${(x^2-y^2)}^2$+4$x^2$$y^2$=$(3{)}^2$+$(-4{)}^2$=25

$\Rightarrow$ ${(x^2+y^2)}^2$=5 ............(ii)

From equation (i) and (ii) $\Rightarrow$ $x^2$=4 $\Rightarrow$x=$\pm$2,

$y^2$=1 $\Rightarrow$y=$\pm$1.Hence the square root of (3-4i)

is $\pm$(2-i).