Question

I^8+i^9+i^10 PLZ EXPLAIN HOW YOU GET THE ANSWER

Answer 1

I^8+i^9+i^10 PLZ EXPLAIN HOW YOU GET THE ANSWER


`i^0= 1\qquad i^1= i\qquad i^2= -1 \qquad i^3= -i \\ \\ \\ i^8= i^3*i^3*i^2 \\ \\ i^8= -i*-i*1\to i^8= i^2*1 \to \qquad \boxed{i^8= 1} \\ \\ \\ i^9= i^3*i^3*i^3 \\ \\ i^9= -i*-i*-i\to i^9= i^2*(-i)\qquad \boxed{i^9= -i} \\ \\ \\ i^1^0= i^3*i^3*i^3*i \\ \\ i^1^0= -i*-i*-i*i\to i^1^0= i^2*(-i^2)\to -1*1\qquad \boxed{i^1^0= -1} \\ \\ \\ i^8+i^9+i^1^0= (1)+(-i)+(-1)= \boxed{-i}`


`\boxed{ i^8+i^9+i^1^0= \boxed{-i} }`