Question

(-i)^13?

Answer 1

i (the imaginary unit) behaves much like any variable, it just has the added condition that
\[\Large \color{green}i^2 = -1\]

Answer 2

So, you could readily say that
\[\Large (-\color{green}i)^{13}=(-1)^{13}\cdot \color{green}i^{13}\]
as the laws of exponents would dictate :)

Answer 3

So it is -i?

Answer 4

yeah

Answer 5

Yeah, that works :D
\[\Large (-1)^{13}=-1\]
\[\Large \color{green}i^{13}=\color{green}{i}^{12}\cdot \color{green}i = \color{green}i\]

Answer 6

IS there a trick to remembering these i's?

Answer 7

Sure there is :)
If you're raising i to some exponent, you might want to divide that exponent by 4, and get the remainder....
for instance, what if we have
\[\Large \color{green}i^{241}\]
If you divide 241 by 4, what remains?

Answer 8

60.25

Answer 9

No, I'm asking for the remainder... but you could use that...

Answer 10

If you're going to do it like that, then use this guide...
if the quotient ends with a .25 (like this one)
then the answer is i

If it ends with a .5 (or .50) then it's -1

If it ends with a .75, then it's -i

And finally, if you get an integer (no decimal part) then it's just 1.

Answer 11

You rock

Answer 12

:)
To avoid confusion, let me just stress that that guide was for i...
your question involved a -i
so just adjust accordingly (like how I separated the -1^13 first)

Answer 13

@terenzreignz , can you also help here?
\[A _{n+1}=2A _{n}+1 \]
for n= 0, 1, 2,

Answer 14

hmm... we need a base step... maybe A0 is already given?

Answer 15

I need to find A4

Answer 16

A0 is 1

Answer 17

Okay, good :)
It REALLY helps to translate the maths terms into English :D

Let's see how to do this...
\[\Large A_{n+1}=2A_n+1\]

Answer 18

A_n simply means the nth term, right?

So what this is telling you, is that every term is twice the previous term, plus 1.
So...
A0 = 1

What's A1?

Answer 19

3?

Answer 20

Very good :)
So now you know that A1 is 3

So what's A2 ?

Answer 21

10?

Answer 22

no... remember... every term is twice the previous term... plus 1...

Answer 23

Duh. Sorry. 7

Answer 24

okay Much better :D

Answer 25

The answer is 31. Thanks.

Answer 26

So reading in english does help!

Answer 27

31?
what...

Answer 28

I need to find A4.
So A2 was 7
A3 is 15
A5 is 31

Answer 29

*A4

Answer 30

ahh okay :D Then that was correct :D

See? You pretty much did it yourself... the key was just understanding the maths problem, and maybe translating it into plain English :P

Answer 31

Thanks