Question

find the value of A and B if$\frac{2 + 3i}{1 + i} = A + iB$

Answer 1

$\bold{\huge{Hay!!}}$

$\bold{Dear\:user!!}$

$\bold{\underline{Question-}}$

find the value of A and B if$\frac{2 + 3i}{1 + i} = A + iB$

$\bold{\underline{Answer-}}$

$\bold{Your\:answer\:is\:\:(A = 5/2,B = 1/2)}$

$\bold{\underline{Explanation-}}$

$\frac{2 + 3i}{1 + i} = A + iB$

$\frac{(2 + 3i)(1 - i)}{(1 + i)(1 - i)} = A + iB \:$

$\frac{2 - 2i + 3i - 3 {i}^{2} }{1 - i {}^{2} } = A + iB \\ \\ \\ \frac{2 + i + 3}{1 + 1} = A + iB \\ \\ \\ \frac{5}{2} + \frac{i}{2} = A + iB \\ \\ \\ A = \frac{5}{2} \: \: \: . \: \: \: \: \: B = \frac{1}{2}$