Question

perform the addition and write the result in standard form. (simplify your answer completely.)
(9 + 5i) + (10 + 11i)

Explanation:

Step1: Group real and imaginary parts

To add complex numbers, we group the real parts and the imaginary parts separately. For \((9 + 5i)+(10 + 11i)\), the real parts are \(9\) and \(10\), and the imaginary parts are \(5i\) and \(11i\). So we can rewrite the expression as \((9 + 10)+(5i+ 11i)\).

Step2: Add real parts and imaginary parts

First, add the real parts: \(9 + 10=19\). Then, add the imaginary parts. When adding like terms with \(i\), we add the coefficients: \(5i+11i=(5 + 11)i = 16i\).

Step3: Combine the results

Now, combine the sum of the real parts and the sum of the imaginary parts to get the result in standard form \(a+bi\), where \(a\) is the real part and \(b\) is the coefficient of the imaginary part. So the result is \(19+16i\).

Answer:

\(19 + 16i\)