A easy complex rule

Algebra Level 2

What is the value of ${ i }^{ 100 }$ in the following the rule : $i=\sqrt { -1 }$

0 -1 i 1

2 solutions

Pedro Henrique
Oct 18, 2015

Following that $i=\sqrt { -1 }$ so ${ i }^{ 4 }=1$

${ i }^{ 100 }={ i }^{ 96 }\ast { i }^{ 4 }\\ { i }^{ 100 }=1*1\\ { i }^{ 100 }=1$

Drex Beckman
Jan 10, 2016

You could also say that i to any even square gives 1, while i to an odd square yields i.

Actually the value of ${i}$ is only 1 when he is a multiple of 4, not all even numbers are multiples of 4, when the number is a multiple of 2, the answer is ${i=-1}$

Pedro Henrique - 5 years, 5 months ago

Okay, but to be fair, the even square thing still works by definition, since all even squares are divisible by 4.

Drex Beckman - 5 years, 5 months ago

Not all even numbers are divisible by 4! Do you THINK that 2 IS DIVISIBLE by 4!

Mohammad Farhat - 2 years, 9 months ago

@Mohammad Farhat – I said all even squares. By that I meant 4, 16, 36, 64, etc. Because any y which can be written as 2x when squared will equal (x^2)*(2^2). Therefore it is divisible by 4.

Drex Beckman - 2 years, 9 months ago

A easy complex rule

2 solutions

0 pending reports