Imaginary!

Algebra Level 2

The value of which of the following numbers is equal to 1?

A. $i^{234}$

B. $i^{128}$

C. $i^{-128}$

D. $i^{-4}$

C and D A B B,Cand D

2 solutions

Syed Baqir
Sep 13, 2015

All of them which are multiples of 4 should give 1.

Such as:

$\color{#D61F06}{ i^{-4} \ , i^{-128} \ and \ i^{128}}$

Proof:

$\Longrightarrow \large i^{4k} = (i^{4})^{k} = 1^{k} = 1$

That's not a proof that all multiples of 4 should give 1.

It should be written as $\LARGE i^{4k}=(i^4)^k=1^k=1$

Isaac Buckley - 5 years, 9 months ago

Well I mean same , I will update the question.

Thanks for the comment :D :D

Syed Baqir - 5 years, 9 months ago

R Dasgupta
Jul 3, 2017

Of course, any ( Positive or Negative) power of i which is divisible by 4 equals 1. Syed's proof shows that.