Question

Evaluate the expression 1 + 3 i/5 i and write the result in the form a + b i .

Answer 1

Answer:   $\bold{\dfrac{3}{5}-\dfrac{1}{5}}i$

Step-by-step explanation:

Rationalize the denominator. Then separate into the a & b-components.

$\dfrac{1+3i}{5i}\bigg(\dfrac{i}{i}\bigg)\quad =\quad \dfrac{i+3i^2}{5i^2}\quad =\quad \dfrac{i+3(-1)}{5(-1)}\quad =\quad \dfrac{i-3}{-5}\quad =\quad \dfrac{3-i}{5}\\\\\\=\large\boxed{\dfrac{3}{5}-\dfrac{1}{5}i}$