evaluate the expression

Question

Evaluate the expression i¹²⁰ and write the results in the form a+bi

the real number a equals?

the real number b equals?

 

Answer 1

 

  i ^120 =( i ^4 ) ^30 = 1 ^30 = 1

Answer 2

Hi Dalia,

 

i¹²⁰=(i²)⁶⁰

      =(-1)⁶⁰

      =1

 

a+bi=1=1+0i

 

a=1  and b=o

Answer 3

We know that i = √-1

so i² = -1. 

i³ = -i

i⁴ = 1

 

This pattern repeats infinitely many times. To determine which power i¹²⁰ corresponds to, divide the exponent by 4 (since the pattern repeats every 4), and whatever the remainder is from this division is the power of i that it corresponds to. 120/4 = 30, with remainder 0, so it corresponds to i⁴  which means i¹²⁰ = 1.

 

Therefore you get 1 +0i where a = 1 and b =0