Question

Perform the indicated operation and write your answer in the form a+bi

(3+2i)^2 - 2(3-i) + 3
a) 9 + 4i
b) 7 + 6i
c) 5 + 8i
d) 11 - 2i

Answer 1

To solve the given expression and write it in the form a+bi, we expanded (3+2i)^2 and -2(3-i) separately then combined the results to get the simplified answer 5 + 14i.

Step-by-step explanation:

The student has asked to perform the indicated operation on a complex number and write the answer in the form a+bi. We are given (3+2i)2 - 2(3-i).

First, let's expand (3+2i)2 which is (3+2i)*(3+2i) = 9+6i+6i+4i2= 9+12i-4 (since i2 = -1).

Next, we expand -2(3-i) to get -6+2i.

Now, let's combine these results: (9+12i-4) + (-6+2i) gives us 5+14i.

This is the simplified form of the original expression in the form a+bi. So, the final answer is 5 + 14i.