Imaginary and complex number help please
Will give medal :).

Question

Imaginary and complex number help please
Will give medal :).

davidusa · Answer

If you go here: http://goo.gl/crNzS7, then you will find Khan academy's exercise on imaginary and complex numbers. I don't understand why all of the numbers are not complex. Can someone help me? :)

davidusa · Answer

Some of the questions aren't what I'm talking about, but the questions I'm talking about look like this.

anonymous · Answer

Is  1+i complex ?

davidusa · Answer

Yes

anonymous · Answer

And i^2 + 1 ?

davidusa · Answer

I dont think so since $$\iota^2 = -1 $$

davidusa · Answer

So there is no more imaginary number.

anonymous · Answer

i^2+1 is a real number. Right ?

davidusa · Answer

Yes. It equals 0.

anonymous · Answer

Good! Now, what is your confusion ?

davidusa · Answer

With this question, and all the similar questions, why aren't all of the choices complex numbers?

hartnn · Answer

can you find $i^4 = .. ?$

davidusa · Answer

Yes. $$\iota^4 = 1$$ because i squared equals -1, and if you square that you get 1.

hartnn · Answer

right, so 6+7i^4 will be real or complex ?

anonymous · Answer

For example since i^4 = 1 $$\sqrt{7} i^{20} = \sqrt{7} (i^4)^5 = \sqrt{7} (1)^5 = \sqrt{7}$$
which is real

davidusa · Answer

It would be real.

hartnn · Answer

correct,
a very quick way to answer those is : 
EVEN exponents of i ----> REAL
ODD exponents of i ----> Complex

davidusa · Answer

Yes, i know that.

kainui · Answer

Since i^4=1 then you can take out multiples of 4.

So i^21 is the same as i^1 because 21 divided by 4 has a remainder of 1.

davidusa · Answer

Also i with even exponents that are a multiple of four equals 1.

hartnn · Answer

thats correct, you already know this stuff :)

kainui · Answer

@DavidUsa Don't forget that powers are really just shorthand for how many of them are multiplied together. $$\large i^{10} = i*i*i*i*i*i*i*i*i*i=(i*i*i*i)(i*i*i*i)(i*i)$$

hartnn · Answer

you still have any doubts ?

davidusa · Answer

Yes, because in a previous question, the correct answer was that i^11+i^12+i^13 was a real number.

hartnn · Answer

thats correct,
can you tell me whats i^11 +i^13 ?

anonymous · Answer

i^11+i^12+i^13 = -i + 1 + i

hartnn · Answer

^

anonymous · Answer

i^11+i^12+i^13 = -i + 1 + i = 1 which is real

hartnn · Answer

you know how i^11 is -i, right ?

davidusa · Answer

Yes.

davidusa · Answer

Oh I understand now thanks a lot.

davidusa · Answer

Sorry i can't give you a medal hartnn I gave it to shail already

hartnn · Answer

hey, no problem! i am not here for medals, if you understand, thats my medal :)

davidusa · Answer

Thanks so much