Question

select all values equivalent to $i^7 \cdot i^2$. select all correct options $\sqrt{-1}$ $-\sqrt{-1}$ $i$ $1$ $-i$

Explanation:

Step1: Add exponents of $i$

$i^7 \cdot i^2 = i^{7+2} = i^9$

Step2: Simplify using $i^4=1$

$i^9 = i^{4 \times 2 + 1} = (i^4)^2 \cdot i^1 = 1^2 \cdot i = i$

Step3: Relate $i$ to radical form

$i = \sqrt{-1}$

Answer:

A. $\sqrt{-1}$, C. $i$