Question

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

Answer 1

assuming you mean $i^{77}$ where $i=\sqrt{-1}$

ok, notice a pattern in the exponent

$i^1=i=\sqrt{-1}$

$i^2=-1$

$i^3=-\sqrt{-1}=-i$

$i^4=1$

$i^5=i=\sqrt{-1}$

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

Answer 2

Answer:

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".