Question

add & subtract complex numbers
(18 + 4i) + (-11 + 23i) =
express your answer in the form (a + bi).

Explanation:

Step1: Add real parts

To add the real parts of the complex numbers, we take the real part of the first complex number, which is \(18\), and the real part of the second complex number, which is \(-11\). Then we add them together: \(18 + (-11)=18 - 11 = 7\).

Step2: Add imaginary parts

Next, we add the imaginary parts. The imaginary part of the first complex number is \(4i\) (so the coefficient of \(i\) is \(4\)) and the imaginary part of the second complex number is \(23i\) (so the coefficient of \(i\) is \(23\)). We add the coefficients: \(4 + 23 = 27\), so the imaginary part is \(27i\).

Step3: Combine real and imaginary parts

Now we combine the real part and the imaginary part we found in the previous steps. The real part is \(7\) and the imaginary part is \(27i\), so the sum of the two complex numbers is \(7 + 27i\).

Answer:

\(7 + 27i\)