Question

i ^2 + i ^3 + i ^4 + i ^5 =

Answer 1

please help

Answer 2

hi

Answer 3

Hi

Answer 4

What did you get for i^2?

Answer 5

mean i squared 2

Answer 6

Right, but do you know how to figure out what i-squared is?

Answer 7

yes

Answer 8

i time i = squared i^2

Answer 9

i is defined to be
\[i=\sqrt{-1}\]so
\[i^2=(\sqrt{1})^2=-1\]
Does that make sense so far?

Answer 10

i^n = i^(n mod4)

Answer 11

Not sure if he knows modular arithmetic...

Answer 12

For u, then:-)

Answer 13

yes

Answer 14

Yeah I remember - thanks!

Answer 15

-1 + -i + 1 + i = 0

Answer 16

Okay, so
\[i^3=(i^2)i=(-1)i=-i\]

Answer 17

Yes, Alchemista, we know, we are showing him how...

Answer 18

yes 4^4 =1?

Answer 19

i^4=1

Answer 20

Yes - i^4= 1

Answer 21

Yep, so now you just add them.

Answer 22

i^5=-1

Answer 23

i^2i^2i = (-1)(-1)i=i

Answer 24

\[i^5=i^4*i=1*i=i\]

Answer 25

That works, too.

Answer 26

yes so its result is 0

Answer 27

correct

Answer 28

Yep.

Answer 29

ok thanks

Answer 30

No worries.