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

Question

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

anthonyym · Answer

Do you know what i is?

mathmale · Answer

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?

anonymous · Answer

yeah sorry I went back and changed it.

mathmale · Answer

While we're on the topic:  i is the imaginary operator, and is the definition of sqrt(-1).

Note the following:$$i^1=i;~ i^2=-1;~ i^3=-i; ~and~i^4=1.  $$

anonymous · Answer

thanks that is really helpful

mathmale · Answer

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

anonymous · Answer

-i

mathmale · Answer

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

anonymous · Answer

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

mathmale · Answer

Thanks, miiles!   :)