Solve the following complex number problems: Write Z1 = -3 + sqrt(-4) and Z2 = 1 − sqrt(-1) in rectangular form.

Here are the solutions to the complex number problems:

Question 1.1

Step 1: Write $Z_1$ and $Z_2$ in a rectangular form.

The rectangular form of a complex number is $a+bi$.
Given $Z_1 = -3 + \sqrt{-4}$ and $Z_2 = 1 - \sqrt{-1}$.
We know that $\sqrt{-1} = i$.
Therefore, $\sqrt{-4} = \sqrt{4 \times -1} = \sqrt{4} \times \sqrt{-1} = 2i$.

$$Z_1 = -3 + 2i$$ $$$$