Question

Perform the indicated operations and reduce to the form a+bi :
1. (5+7i)+(8+2i).

Answer 1

To add the complex numbers (5+7i) and (8+2i), we simply add their real parts to get 13, and their imaginary parts to get 9i. The result is the complex number 13+9i.

Step-by-step explanation:

To perform the indicated operations and reduce to the form a+bi, we will add the two complex numbers (5+7i) and (8+2i). We do this by adding the real parts together and the imaginary parts together.

Step 1: Add the real parts. 5 (real part of the first complex number) plus 8 (real part of the second complex number) equals 13.

Step 2: Add the imaginary parts. 7i (imaginary part of the first complex number) plus 2i (imaginary part of the second complex number) equals 9i.

Combining the results of these two steps gives us 13+9i, which is already in the standard form for a complex number, a+bi.