Given Z1 = 2+3i and Z2 = 2−i. Express racZ1Z2 in the form a+bi where a,b R.

Here are the solutions for the complex number problems:

Question 26:
Given $Z_1 = 2+3i$ and $Z_2 = 2-i$.

a) Express $\frac{Z_1}{Z_2}$ in the form $a+bi$ where $a,b \in \mathbb{R}$.

Step 1: Substitute the given values for $Z_1$ and $Z_2$ and multiply by the conjugate of the denominator.

$$\frac{Z_1}{Z_2} = \frac{2+3i}{2-i}$$ $$$$