Question

Express (3+4i) ^-1 in the form x+iy

Answer 1

${(3 + 4i})^{ - 1} \\ = \frac{1}{3 + 4i} \\ = \frac{1}{3 + 4i} \times \frac{3 - 4i}{3 - 4i} \\ = \frac{3 - 4i}{ {3}^{2} - ( {4i})^{2} } \\ = \frac{3 - 4i}{9 + 16} \\ = \frac{3 - 4i}{25} \\ = \frac{3}{25} - i\frac{4}{25} \\ here \: \: \: a = \frac{3}{25} \: \: \: \: b = \frac{ - 4}{25}$