Question

Which of the following is equivalent to the complex number i^7?
a.1 b. i c.-1 d.- i

Answer 1

Do you know what i is?

Answer 2

I found this question confusing until I realized that you meant i^7, or \[i^7.\] That makes a BIG difference.

Note that i^7=i^4*i^3. What is i^3 equivalent to?

Answer 3

yeah sorry I went back and changed it.

Answer 4

While we're on the topic: i is the imaginary operator, and is the definition of sqrt(-1).

Note the following:\[i^1=i;~ i^2=-1;~ i^3=-i; ~and~i^4=1. \]

Answer 5

thanks that is really helpful

Answer 6

This pattern repeats itself.

So, if you start with i^7, you can replace that with i^3. What is i^3?

Answer 7

-i

Answer 8

Yes. so now you can choose the correct answer choice. nice work!

Answer 9

thank you so much, I'll give you a medal!!

Answer 10

Thanks, miiles! :)