Question

What is the simplified form of i^13

Answer 1

Answer:

i

Step-by-step explanation:

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

Multiplying by i repeats the pattern .

Thus, any i⁴ⁿ = 1

If n = 3, 4n = 12, so

i¹² = 1 and

i¹³ = i¹ = i