Complex number:solve --> i^5(8i^2 - 7i^3)

answer
-7 - 8i

I guess you are asking how to get that answer?
First distribute, giving this result. 8i^7-7i^8
Then all powers of i can be reduced to either 1, -1, i, or, -i.
i^7=(i*i)*(i*i)*(i*i)*i=-1*-1*-1*i=-i. So that is how you get the -8i
then in the same way you find that i^8 =-i
Remember - since i=sqrt(-1), i*i=-1

i^5(8i^2 - 7i^3)

i^5*(8 i^2) - i^5 * (7i^3)

8 i ^ 7 - 7 i ^ 8

since i^2 = -1

8i^7 - 7 i^8 = - 8 i - 7

i^5(8i^2 - 7i^3)
= 8 i^7 - 7 i^8
= 8 ( -1^3 i ) - 7( -1 ^4 )
= 8 ( -1 i) - 7 ( 1 )
= -8i - 7

*rem i^2 = -1

i^5(8i^2 - 7i^3)
= 8i^7 - 7i^8
= -7 - 8i