Question

Find the value of i77.
A) 1
B) i
C) −1
D) −i

Answer 1

The correct answer is B

Step-by-step explanation: I remember from my algebra 2 class, you divide the powers by 4, and it should give you 194.5. When your decimal is .5 that means it is a positve "i".

Answer 2

assuming you mean
`i^(77)` where
`i=√(-1)`

ok, notice a pattern in the exponent

`i^1=i=√(-1)`

`i^2=-1`

`i^3=-√(-1)=-i`

`i^4=1`

`i^5=i=√(-1)`

hum, so it goes 1,2,3,4, then repeats

ok, so every 4, the cycle repeats

how far up is 77 from a multipule of 4?

4*19=76

76 is 1 away from 77

so
`i^(77)=(i^(76))(i^1)=`

`(i^4)^(19)(i)=(1)^(19)i=i`

the answer is B