Given A = (4 − 2i)2, B = (3 + 2i)3. Evaluate A + B

Sure, let's solve this step by step.

Step 1: Solve for A A = (4 - 2i)^2 = (4 - 2i) * (4 - 2i) = 16 - 8i - 8i + 4 = 20 - 16i

Step 2: Solve for B B = (3 + 2i)^3 = (3 + 2i) * (3 + 2i) * (3 + 2i) = (9 + 6i + 6i + 4) * (3 + 2i) = (13 + 12i) * (3 + 2i) = 39 + 26i + 36i + 24 = 63 + 62i

Step 3: Add A and B A + B = (20 - 16i) + (63 + 62i) = 20 + 63 - 16i + 62i = 83 + 46i

So, A + B = 83 + 46i.

Sure, let's solve this step by step.

Step 1: Solve for A A = (4 - 2i)^2 = (4 - 2i) * (4 - 2i) = 16 - 8i - 8i + 4 = 20 - 16i

Step 2: Solve for B B = (3 + 2i)^3 = (3 + 2i) * (3 + 2i) * (3 + 2i) = (9 + 12i + 4) * (3 + 2i) = (13 + 12i) * (3 + 2i) = 39 + 26i + 36i - 24 = 15 + 62i

Step 3: Add A and B A + B = (20 - 16i) + (15 + 62i) = 35 + 46i

So, A + B = 35 + 46i.