the dirrections say perform the operations. I got 14i+4i^2 but got it wrong. Please help?

Question

the dirrections say perform the operations. the question was 2i(7+2i) And I got 14i+4i^2 but the teacher wrote finish on it and ask me to redo it. i did not think you could combine the terms since one is squared and the other is not. What do I do

Also with the same instructions there is a question (3i)^2 and I got 9i^2 and the teacher wrote finnish on it what else can I do to this

Answer 1

So close:

i^2 = (sqrt(-1))^2 = -1

So, to finish the first problem,

14i + 4i^2 = 14i - 2

Similarly, to finish your second problem, replace i^2 = -1.

Answer 2

Remember that the term i stands for the square root of negative one. When you distribute the 2i to the (7+2i) The 2i*2i becomes 2*1. This is because when you multiply the two i's (sqrt(-1)*(sqrt(-1) you get -(1) (The roots cancel.) That is why your teacher said to finish it. Its a bit confusing but your final should be 14i-1. I hope that helped.