How can we simplify the expression 4 + 2i + 1 + 7i?

To simplify the expression 4 + 2i + 1 + 7i, we need to combine like terms. Start by grouping the real numbers and the imaginary numbers separately.

The real numbers in the expression are 4 and 1. When we add these together, we get:

4 + 1 = 5

Next, we look at the imaginary numbers, which are 2i and 7i. Adding these gives us:

2i + 7i = 9i

Now we combine the results from both parts. The simplified expression is:

5 + 9i

So, the answer is 5 + 9i.