Question

Find:

$\sqrt{8-6i}=$

• A. $\pm (3+i)$
• B. $\pm (3-i)$
• C. $\pm (2+i)$
• D. $\pm (2-1)$

Answer 1

The correct option is B $\pm (3-i)$

Let $\sqrt{8-6i}=x+iy8-6i=(x+iy{)}^2=x^2+i^2{y}^2+2yi$

$8-6i=x^2-y^2+2xyi$ Since $i^2=-1.$

$x^2-y^2=8x^2{\left(\frac{-3}{x}\right)}^2=8x^2-\frac{9}{x^2}=8x^4-8x^2-9=0x^4-9x^2+x^2-9=0x^2-1=0,x^2-9=0x^2=-1,x^2=9x=i,x=3,-3y=-1,1$ $2xy=-6xy=-3y=\frac{-3}{x}$

$\therefore x=3,y=-1$ or $x=-3,y=1$

$\sqrt{8-6i}=3-i$ or $-3+i$

$\sqrt{8-6i}=\pm (3-i)$