Question

What is the simplified form of i^13

Answer 1

i

Explanation:

`\begin{array}{lclcr}i^(1) & = &(√(-1))^(1)&=& i\\i^(2) & = & (√(-1))^(2)& =&-1\\i^(3) & = & (√(-1))^(3)&=&-i\\i^(4) & = & (√(-1))^(4)& = &1\\\end{array}`

Multiplying by i repeats the pattern .

Thus, any i⁴ⁿ = 1

If n = 3, 4n = 12, so

i¹² = 1 and

i¹³ = i¹ = i