Question

Calculate the power of i. i ^48

Answer 1

\(\bf \textit{what's }i^2?\)

Answer 2

-1

Answer 3

\(\bf 48\div 2 = 24\implies 24\cdot 2=48\\ \quad \\ \quad \\

i^{48}\implies (i^2)^{24}\implies (-1)^{24}\)

what do you think?

Answer 4

Ugh, I don't know. I wasnt there for the lesson. Wouldn't it be -1 still??

Answer 5

well, -1 * -1 = ?

Answer 6

1

Answer 7

yeap

if you multiply -1 an EVEN number of times, your result will be +1
if you multiply -1 an ODD number of times, then you'd get -1

notice \(\bf 48\div 2 = 24\implies 24\cdot 2=48\\ \quad \\ \quad \\

i^{48}\implies (i^2)^{24}\implies (-1)^{{\color{red}{ 24}}}\implies (-1)(-1)...{\color{red}{ 24}}\ times\)

Answer 8

so it would be 1 because the 24 is even?

Answer 9

yeap

Answer 10

okay so for any question that asks me to calculate the power of i I just divide it by 2????

Answer 11

yeap
you set it firstly as an exponential with a \(\bf i^2\)

because say for example \(\bf i^6\implies i^2\cdot i^2\cdot i^2\implies -1\cdot -1\cdot -1\implies -1
\\ \quad \\
i^6\implies (i^2)^{\color{red}{3}}\)

so even though the original exponent is EVEN, 6
the result is -1
if you don't set it up first as \(i^2\)

Answer 12

okay. I have this problem. i^ 361 what do I do since its an odd number??

Answer 13

let's see 361/2 = 180.5
so
we can use 180 safely
so 180 * 2 = 360 so

\(\bf i^{361}\implies i^{360}\cdot i^1\implies (i^2)^{{\color{red}{ 180}}}\cdot i^1\implies +1\cdot i\implies i\)

Answer 14

thanks

Answer 15

yw