Question

If i=sqr-1, what is the value of i^3? -1 i 1 -i

Answer 1

Answer:

After solving we get $\mathbf{i^3=-i}$

Option D is correct.

Step-by-step explanation:

We are given:

If  $i=\sqrt{-1}$ we need to find the value of $i^3$

Solving:

$i=\sqrt{-1}$

Taking cube on both sides

$i^3=(\sqrt{-1})^3$

We can write $a^3= a^2.a^1$ Using this for solving:

$i^3=(\sqrt{-1})^2.(\sqrt{-1})\\We \ know \ (\sqrt{-1})^2 =- 1 \ and \ \sqrt{-1}=1 \\i^3=-1(i)\\i^3=-i$

So, after solving we get $\mathbf{i^3=-i}$

Option D is correct.