Evaluate: `(1-i+i^2)^(-15)`

Evaluate: (i) int(a^x)/(sqrt(1-a^(2x)))\ dx

Evaluate: i^37 + 1/i^67 .

Evaluate: ( i^31 + frac{1}{i^67} )

Evaluate [i^18 + (1/i)^25]^3

Evaluate sum_(i=1)^13( i^n + i^(n+1) ) where, n in N

Find the value of (1 + i)^(2 / 3) using De Moivre's Theorem.

Solve the following: Find the value of ((1 + i)^(2n) - (1 - i)^(2n)) / ((1 + omega^4 - omega^2) (1 - omega^4 + omega^2))

Find the modulus and amplitude of the following complex numbers: (1 + 2i)^2 (1 - i)

Find the value of: 1+ i^2 + i^4 + i^6 + i^8 +............+ i^20