Question

Simplify i38

Answer 1

@ganeshie8

Answer 2

is that \(\large i^{38}\)
?

where i is the square root of -1 ?

Answer 3

yes thats it

Answer 4

cool,
so \(i=\sqrt{-1}\)

square both sides , what u get ?

Answer 5

1?

Answer 6

naah,
\(i=\sqrt{-1} \\ \implies i^2 =(\sqrt{-1} )^2= -1 \)

got that ?

Answer 7

So its not positive its negative 1 ? I got the steps, im taking it down. thankyou

Answer 8

sure,

so, \(i^2 =-1 \)
now square both sides again! to get i^4 =...?

Answer 9

you lost me there, is that a separate problem ?

Answer 10

nopes, we are still trying to find i^38

for that we will need , i^2 and i^4

we got i^2 =-1

to get i^4, we just square both sides.

so, \(i^2=-1 \\ \implies (i^2)^2= (-1)^2 \\ \implies i^4 =1\)

got this ?

Answer 11

because -1 * -1 =1

Answer 12

I got the answer to be i is that correct?

Answer 13

lets check ,

\(i^{38}= i^2 \times i^{36}= i^2 \times (i^4)^9 =-1 \times (1)^9=-1\)

i am getting -1
how u got i?

Answer 14

with those steps i also got -1 so lets see if its correct

Answer 15

i selected -1