# Math Help - complex numbers

1. ## complex numbers

the question is:
write each of the following in the form x+yi, wherre x and y are real numbers:

i^12+i^15

as my for i^12 i get 1 but for i^15 im not sure i think its -1 (ixi)

and can you please answear i^7-i^11 - dont anderstand the answear, how they both=0

thnx

2. Powers of i are "periodic with period 4". That is, $i^0= 1$, $i^1= i$, $i^2= -1$, $i^3= (i^2)(i)= -i$, and $i^4= (i^2)(i^2)= (-1)(-1)= 1$ and now everything repeasts.

4 divides into 15 3 times with remainder 3: 3(4)+ 3= 12+ 3= 15. That means that $i^{15}= i^{4+ 4+ 4+ 3}= i^4(i^4)(i^4)(i^3)= 1(1)(1)(i^3)= i^3= -i$.

7= 4+ 3 and 11= 4+ 4+ 3 so $i^7= (1)i^3= -i$ and $i^{11}= (1)(1)(i^3)= -i$. They don't "both = 0". They both equal -i so their difference is 0.