Question

Which is equivalent to (2-3i)(i³⁰³)?

Answer 1

-2i - 3

I can't see a simpler way to explain it. You just have to work your way through each step.

Explanation:

The question is what is i^303?

Remember that when the power is divisible by 4 the expression changes to 1

i^1 = i

i^2 = i * i = sqrt(-1)*sqrt(-1) = - 1

i^3 = i^2 * i = - i

i^4 = i^2 * i^2 = -1 * - 1 = 1

So what does i^303 =

i^300 * i^3

But 300 is evenly divisible by 4. (300 / 4 = 75) so i^300 = 1^75

i^3 = -i

So now you are ready to do the question

(2 - 3i) * -i

2*-i - 3i(-i)

-2i - 3(i^2 * - 1)

-2i - 3(-1 * - 1)

-2i - 3(1)

-2i - 3