Question

If i is raised to an odd power, then it can not simplify to be

1. -1

2. -i

3. i

Answer 1

Answer:

1. -1

Step-by-step explanation:

Since we know that i is an imaginary number. We also know that $i=\sqrt{-1}$ and $i^2=-1$.

Let us see i raised to different powers.

$i^3=i^2\cdot i$

$i^3=-1\cdot i$

$i^3=-i$

$i^4=i^2\cdot i^2$

$i^4=-1\cdot -1$

$i^4=1$

$i^5=i^4\cdot i$

$i^5=1 \cdot i$

$i^5= i$

$i^6=i^4\cdot i^2$

$i^6=1 \cdot -1$

$i^6=-1$

$i^7=i^4\cdot i^3$

$i^7=1\cdot -i$

$i^7=-i$

$i^8=i^4\cdot i^4$

$i^8=1\cdot 1$

$i^8=1$

$i^9=i^5\cdot i^4$

$i^9=i\cdot 1$

$i^9=i$

We can see that when we raise i to 3rd power and 7th power we got -i and when we raised i to 5th and 9th power we got i.

Therefore, if we raise i to an odd power, it can not simplify to be -1 and 1st option is the correct choice.

Answer 2

Answer:

-1

Step-by-step explanation:

If i is raised to an odd power, then it can not simplify to be

-1

-i

i

Odyssey