what is the value of $5^{3}i^{9}$?\n- $- 125i$\n- $-15i$\n- $15i$\n- $125i$

Explanation:

Step1: Calculate $5^3$

$5^3=5\times5\times5 = 125$

Step2: Simplify $i^9$

We know that $i^1 = i$, $i^2=- 1$, $i^3=i^2\times i=-i$, $i^4=(i^2)^2 = 1$. Since $9 = 4\times2+1$, then $i^9=(i^4)^2\times i=1^2\times i = i$

Step3: Calculate $5^3i^9$

$5^3i^9=125\times i=125i$

Answer:

$125i$