algebra

Quote:

(1+2i)^2-2(1+2i)+5

If you mean i as in i = sqrt(-1) then

(1+2i) ² = (1+2i)(1+2i) = (1-4) + (2+2)i = -3+4i

2(1+2i) = 2+4i

so

(1+2i)^2-2(1+2i)+5 = (-3+4i) - (2+4i) + 5 = (-3 - 2 + 5) + (4-4)i = 0

If on the other hand you mean just some variable called i

(1+2i) ² = 1 + 4i + 4i ²

2(1+2i) = 2 + 4i

so

(1+2i)^2-2(1+2i)+5 = (1 + 4i + 4i ²) - (2 + 4i) + 5 = 4i ² + (4 - 4)i + (1 - 2 + 5) = 4i ² + 4 = 4(i ²+1)

The first part is what i was going with. I didn't think about (1+2i)(1+2i) and foil and now I feel really dumb for not thinking of it earlier. I got the same answer but through a different method. Thanks