Question

What is the value of the expression i 0 × i 1 × i 2 × i 3 × i 4?

Answer 1

`\bf \stackrel{\stackrel{1}{}}{i^0}* \stackrel{\stackrel{i}{}}{i^1}* \stackrel{\stackrel{-1}{}}{i^2}* \stackrel{\stackrel{-i}{}}{i^3}* \stackrel{\stackrel{1}{}}{i^4}\implies 1\cdot i\cdot -1\cdot -i\cdot 1\implies i^2\implies -1`

Answer 2

Answer: The required value of the give expression is -1.

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

`E=i^0* i^1* i^2* i^3* i^4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~``(i)`

We know that

`i` is an imaginary number where :

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

So, we get from (i) that

`E\\\\=i^0* i^1* i^2* i^3* i^4\\\\=1* i* (-1)* (-i)*1\\\\=i^2\\\\=-1.`

Thus, the required value of the give expression is -1.