Question

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

Answer 1

$\bf \stackrel{\stackrel{1}{}}{i^0}\times \stackrel{\stackrel{i}{}}{i^1}\times \stackrel{\stackrel{-1}{}}{i^2}\times \stackrel{\stackrel{-i}{}}{i^3}\times \stackrel{\stackrel{1}{}}{i^4}\implies 1\cdot i\cdot -1\cdot -i\cdot 1\implies i^2\implies -1$

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 :

$E=i^0\times i^1\times i^2\times i^3\times i^4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~``(i)$

We know that

$i$ is an imaginary number where :

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

So, we get from (i) that

$E\\\\=i^0\times i^1\times i^2\times i^3\times i^4\\\\=1\times i\times (-1)\times (-i)\times1\\\\=i^2\\\\=-1.$

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