Full solution

(-13+16 i)-(3+4 i)=

\newline

Express your answer in the form

(a+b i)

Identify complex numbers: Identify the real and imaginary parts of each complex number. $\newline$ The first complex number is $(-13+16i)$ , where $-13$ is the real part and $16i$ is the imaginary part. $\newline$ The second complex number is $(3+4i)$ , where $3$ is the real part and $4i$ is the imaginary part.
Subtract real parts: Subtract the real parts of the complex numbers. $\newline$ Subtract the real part of the second complex number from the real part of the first complex number. $\newline$ Real part calculation: $(-13) - (3) = -13 - 3 = -16$
Subtract imaginary parts: Subtract the imaginary parts of the complex numbers. $\newline$ Subtract the imaginary part of the second complex number from the imaginary part of the first complex number. $\newline$ Imaginary part calculation: $(16i) - (4i) = 16i - 4i = 12i$
Combine real and imaginary parts: Combine the results of the real and imaginary parts. $\newline$ Combine the results from Step $2$ and Step $3$ to get the final answer in the form $(a+bi)$ . $\newline$ Final answer: $(-16) + (12i)$ = $-16$ + $12$ i