Question

What is the value of the expression i^0 x i^1 x i^2xi^3xi^4

Answer 1

The value of given expression is -1.

Explanation:

We have to evaluate the following expression:

`i^0* i^1* i^2* i^3* i^4`

We know that:

`i = √(-1)\\i^2 = -1\\i^3 = -i\\i^4 = 1`

Putting the values in the expression:

`i^0* i^1* i^2* i^3* i^4\\=1* i* -1* -i* 1\\= i^2\\= -1`

Hence, the value of given expression is -1.

Answer 2

Answer: The answer is - 1.

Step-by-step explanation: We are given to find the value of the given expression

`E_c=i^0* i^1* i^2* i^3* i^4.`

We know that 'i' is an imaginary unit and its value is √-1. So, we have

`i^0=(√(-1))^0=1,\\\\i^1=i=√(-1),\\\\i^2=(√(-1))^2=-1,\\\\i^3=i^2.I=(-1)i=-√(-1),\\\\i^4=(i^2)^2=(-1)^2=1.`

Therefore, the given expression becomes

`E_c\\\\=i^0* i^1* i^2* i^3* i^4\\\\=1* √(-1)*(-1)*({-√(-1)})* 1\\\\=1* (-1)\\\\=-1.`.

Thus, the answer is - 1.