Question

Given (2-i3) =
$\sqrt{a + ib}$
find a and b
​

Answer 1

Answer:

$(2-i3) = \sqrt{a + ib} \\ {(2-i3)}^{2} = {( \sqrt{a + ib})}^{2} \\ {2}^{2} - 6i - {(3i)}^{2} = a + ib \\ 4 - 6i + 9 = a + ib \\ 13 - 6i= a + ib \\ \color{red} \boxed{a = 13 }\\ \color{yellow} \boxed{b = - 6}$