In Exercises 53–60, write each power of i as as i, - 1, - i, or 1...

Question

In Exercises 53–60, write each power of i as as i, - 1, - i, or 1.

i^44

Accepted Answer

Welcome back. I'm so glad you're here. We've got this gorgeous number here. I to the 88th is our expression and we are to write it as negative. 11 negative I or I. Well how do we do that? We recall from previous lessons that when we have I to the first that equals I. When we have I to the second that equals negative one. When we have I to the third that equals negative I and I to the fourth equals positive one. Well those are our four answer choices. But how do we get from 88 to any of those four choices? Well, the key here is this I to the fourth equals one. We want to know how many ones are in I to the 88th. Or in other words how many I to the fourths are in I to the 88th because one times however many ones it is. That's just going to be one. So let's find out how many I to the fourths are an eye to the 88th by dividing 88 by four. While we plug that into a calculator and 88 divided by four is 22. Alright, well there are 22 I. to the fourths and I to the 88 Or in other words we've got I to the fourth raised to the 22nd and I to the fourth again, that's just one. So one raise to the 22nd and one times however many ones it's going to be. That's just one. So our answer here is answer choice. B Well done. We'll catch you on the next one.

In Exercises 53–60, write each power of i as as i, - 1, - i, or 1. i^44

Key Concepts

Powers of i

Modulus and Division

Complex Numbers

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