Question

express in the form of a+ib :(1/3+3i)

Answer 1

$\frac{1}{3 + 3i} \\ = \frac{1}{3 + 3i} \times \frac{3 - 3i}{3 - 3i} \\ = \frac{3 - 3i}{(3 + 3i)(3 - 3i)} \\ = \frac{3 -3i}{ {3}^{2} - {( 3i)}^{2} } \\ = \frac{3 -3i}{9 - 9 {i}^{2} } \\ = \frac{3 + 3i}{9 - 9( - 1)} \\ = \frac{3 - 3i}{9 + 9} = \frac{3 - 3i}{18} \\ = \frac{1 - i}{6} \\ = \frac{1}{6} - \frac{1}{6} i$