$(8-10 i)-(-16+2 i)=$ $\newline$ Express your answer in the form $(a+b i)$ .

Full solution

(8-10 i)-(-16+2 i)=

\newline

Express your answer in the form

(a+b i)

Identify numbers to subtract: Identify the numbers to be subtracted. $\newline$ We have two complex numbers: $(8-10i)$ and $(-16+2i)$ . We need to subtract the second complex number from the first one.
Change subtraction to addition: Change the subtraction to addition by distributing the negative sign to the second complex number. $\newline$ $(8-10i) - (-16+2i)$ becomes $(8-10i) + (16-2i)$ when we distribute the negative sign.
Combine real parts: Combine the real parts of the complex numbers. $\newline$ The real part of the first complex number is $8$ , and the real part of the second complex number is $16$ . Adding these together gives us $8 + 16$ .
Calculate sum of real parts: Calculate the sum of the real parts. $8 + 16 = 24$ .
Combine imaginary parts: Combine the imaginary parts of the complex numbers. $\newline$ The imaginary part of the first complex number is $-10i$ , and the imaginary part of the second complex number is $-2i$ . Adding these together gives us $-10i - 2i$ .
Calculate sum of imaginary parts: Calculate the sum of the imaginary parts. $-10i - 2i$ equals $-12i$ .
Combine results in $(a+bi)$ form: Combine the results of the real and imaginary parts to express the answer in the form $(a+bi)$ . $\newline$ The real part is $24$ and the imaginary part is $-12i$ , so the final answer is $24 - 12i$ .