Evaluate [i^18+(1/i)^25]^2 .

Answer 1

i^2 = -1, i^4 = 1, i^16 = 1, i^2 = -1, if the exponent of i is divisible by 4, it = 1

i^16 x i^2 = 1 x -1 = -1

i^a x i^b = i^a+b. add the exponents, 16+2 = 18

i^16 x i^2 = i^18

i^18 =i^16 x i^2 = -1

i^25 = i^24 x i = 1 x i = i

i^25 = i

1/i = -i

1/i = (1/i)(i/i) = i/-1 =-i

(-1 +ii)^2 =(-1-i)(-1-i) = (1+i)(1+i) = 1 +2i -1 = 2i

[i^18 + 1/i^25]^2 = 2i

= 2 times the square root of -1