Respuesta :
Answer: The answer is - 1.
Step-by-step explanation: We are given to find the value of the given expression
[tex]E_c=i^0\times i^1\times i^2\times i^3\times i^4.[/tex]
We know that 'i' is an imaginary unit and its value is √-1. So, we have
[tex]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.[/tex]
Therefore, the given expression becomes
[tex]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.[/tex].
Thus, the answer is - 1.
Answer:
The value of given expression is -1.
Step-by-step explanation:
We have to evaluate the following expression:
[tex]i^0\times i^1\times i^2\times i^3\times i^4[/tex]
We know that:
[tex]i = \sqrt{-1}\\i^2 = -1\\i^3 = -i\\i^4 = 1[/tex]
Putting the values in the expression:
[tex]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[/tex]
Hence, the value of given expression is -1.
