Question

Which of the following is equivalent to the complex number i^34 ?

Choose 1 answer:
А
1
B I
C
-1
D
-I

Answer 1

Given:

The complex number is
`i^(34)`.

To find:

The value of given complex number.

Solution:

We have,

`i^(34)`

It can be written as

`i^(34)=i^(32+2)`

Using properties of exponents, we get

`i^(34)=i^(32)i^(2)`
`[\because a^(m+n)=a^ma^n]`

`i^(34)=i^(4* 8)i^(2)`

`i^(34)=(i^4)^8i^(2)`
`[\because (a^(m))^n=a^(mn)]`

We know that,
`i^4=1,i^2=-1`.

`i^(34)=(1)^8(-1)`

`i^(34)=(1)(-1)`

`i^(34)=-1`

The value of
`i^(34)` is -1. Therefore, the correct option is C.