Question

1. $7 + 2i + (4 + 3i)$

Explanation:

Step1: Remove parentheses

To add complex numbers, we first remove the parentheses. The expression \(7 + 2i+(4 + 3i)\) becomes \(7 + 2i+4 + 3i\) since there is a plus sign in front of the parentheses, so we don't change the signs inside.

Step2: Combine real parts and imaginary parts

Next, we combine the real parts (the terms without \(i\)) and the imaginary parts (the terms with \(i\)) separately.
For the real parts: \(7+4 = 11\).
For the imaginary parts: \(2i + 3i=(2 + 3)i=5i\) (using the distributive property \(ai+bi=(a + b)i\) for complex numbers).

Step3: Combine the results

Now we combine the results of the real and imaginary parts. So \(11+5i\) is the simplified form of the given complex number addition.

Answer:

\(11 + 5i\)