Question

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

Answer 1

Answer: The answer is - 1.

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

$E_c=i^0\times i^1\times i^2\times i^3\times i^4.$

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

$i^0=(\sqrt{-1})^0=1,\\\\i^1=i=\sqrt{-1},\\\\i^2=(\sqrt{-1})^2=-1,\\\\i^3=i^2.I=(-1)i=-\sqrt{-1},\\\\i^4=(i^2)^2=(-1)^2=1.$

Therefore, the given expression becomes

$E_c\\\\=i^0\times i^1\times i^2\times i^3\times i^4\\\\=1\times \sqrt{-1}\times(-1)\times({-\sqrt{-1}})\times 1\\\\=1\times (-1)\\\\=-1.$.

Thus, the answer is - 1.

Answer 2

Answer:

The value of given expression is -1.

Step-by-step explanation:

We have to evaluate the following expression:

$i^0\times i^1\times i^2\times i^3\times i^4$

We know that:

$i = \sqrt{-1}\\i^2 = -1\\i^3 = -i\\i^4 = 1$

Putting the values in the expression:

$i^0\times i^1\times i^2\times i^3\times i^4\\=1\times i\times -1\times -i\times 1\\= i^2\\= -1$

Hence, the value of given expression is -1.