Question

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

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

$i^{34}=i^{32}i^{2}$            $[\because a^{m+n}=a^ma^n]$

$i^{34}=i^{4\times 8}i^{2}$

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

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.