Question

Given (2-i3) =

`√(a + ib)`
find a and b
​

Answer 1

`(2-i3) = √(a + ib) \\ {(2-i3)}^(2) = {( √(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}`