$(-3+71 i)+(9)=$ $\newline$ Express your answer in the form $(a+b i)$ .

Full solution

(-3+71 i)+(9)=

\newline

Express your answer in the form

(a+b i)

Identify numbers to be added: Identify the numbers to be added. $\newline$ We have two numbers: a complex number $(-3+71i)$ and a real number $9$ . The real number can be thought of as a complex number with an imaginary part of $0$ , so it is $9 + 0i$ .
Add real parts of complex numbers: Add the real parts of the complex numbers. $\newline$ The real part of $(-3+71i)$ is $-3$ , and the real part of $9 + 0i$ is $9$ . Adding these together gives us $-3 + 9$ .
Perform addition of real parts: Perform the addition of the real parts. $\newline$ Calculating $-3 + 9$ gives us $6$ .
Add imaginary parts of complex numbers: Add the imaginary parts of the complex numbers. $\newline$ The imaginary part of $(-3+71i)$ is $71i$ , and the imaginary part of $9 + 0i$ is $0i$ . Adding these together gives us $71i + 0i$ .
Perform addition of imaginary parts: Perform the addition of the imaginary parts. $\newline$ Calculating $71i + 0i$ gives us $71i$ .
Combine real and imaginary parts: Combine the results of the real and imaginary parts. $\newline$ We combine the real part $6$ and the imaginary part $71i$ to express the sum in the form $(a+bi)$ .
Write final answer: Write the final answer. $\newline$ The sum of $(-3+71i)$ and $9$ is $6 + 71i$ .