$(10-22 i)+(22 i)=$ $\newline$ Express your answer in the form $(a+b i)$ .

Full solution

(10-22 i)+(22 i)=

\newline

Express your answer in the form

(a+b i)

Identify complex numbers: Identify the real and imaginary parts of the complex numbers. $\newline$ The real part of the first complex number is $10$ , and the imaginary part is $-22i$ . The second complex number has no real part and an imaginary part of $22i$ .
Add real parts: Add the real parts together. $\newline$ Since the second complex number has no real part, the real part of the sum is just the real part of the first complex number, which is $10$ .
Add imaginary parts: Add the imaginary parts together. $\newline$ The imaginary parts are $-22i$ and $22i$ . When we add them together, they cancel each other out because $-22i + 22i$ equals $0i$ .
Combine real and imaginary parts: Combine the sum of the real parts and the sum of the imaginary parts. $\newline$ The sum of the real parts is $10$ , and the sum of the imaginary parts is $0i$ . Therefore, the sum of the two complex numbers is $10 + 0i$ .
Express answer in $(a+bi)$ form: Express the answer in the form $(a+bi)$ . $\newline$ Since the imaginary part is $0$ , the expression simplifies to just the real part, which is $10$ . So the answer in the form $(a+bi)$ is $10 + 0i$ , which can be written simply as $10$ .