How do I evaluate (1+i)2+i(1+i)2+i?

Answer 1

Assuming that the i is a variable and not an imaginary number.

To start, we can rearrange the equation to get a better idea of what is going on. Let move all the multiplications to the front of the parenthesis.

2(1+i)+2i(1+i)+i

Following the order of operations, we will solve the multiplication first. This is done by multiplying each value inside the parenthesis with the value outside the parenthesis.

(2 + 2i) + (2i + 2i²)+ i

Notice that the parenthesis are no longer necessary, so we will get rid of them.

2 + 2i + 2i + 2i² + i

Now all that is left is to combine like terms. We will order the terms by exponent size.

2i² + 5i + 2

Answer 2

Distribute. Then combine like-terms.

In the first set of terms (1 + i)2, multiply 2 x 1 and 2 x i to get 2 + 2i

In the second set of terms, i(1 + i), multiply i x 1 and i time i to get i + i² (but i² = -1) or -1 + i. I don't know if you have a typo or not in this second set of terms. Is it really then multiplied by 2? If so, it would become 2 times the previous results or 2 x -1 and 2 x i to be -2 + 2i

Then add i

Add all the numbers and then all the i's

I suspect you typed something incorrectly though. Please double check.