Question

Divide:$\frac{3+3i}{2i}$

Short answer

The answer of the above equation is$\frac{3}{2}-\frac{3}{2}i$

Step-by-step solution

Given information

We are given an expression$\frac{3+3i}{2i}$

Write denominator in standard form

We get,$\frac{3+3i}{0+2i}$

 Multiply the numerator and denominator bythe complex conjugate of the denominator.

$\frac{3+3i}{0+2i}\times \frac{0-2i}{0-2i}$

Multiply and simplify the real and imaginary terms

$$\begin{gathered} \frac{6i-6i^2}{-4i^2} \\ \frac{6i-6(-1)}{-4(-1)} \\ \frac{6-6i}{4} \end{gathered}$$

Rewrite in standard form

We get,$\frac{3}{2}-\frac{3}{2}i$

Conclusion

The answer of the above expression is$\frac{3}{2}-\frac{3}{2}i$