Algebra Conundrum ( i and pi)

Algebra Level 1

$0! \times 𝑖^2 \times \pi = ?$

Note: Round $\pi$ in this equation to the nearest hundredth.

0.314 -3.14 3.14 𝑖⁴ 0 (π²) 𝑖 -𝑖⁴

1 solution

Prakash Kallanmarthodi
Oct 11, 2019

The Factorial of 0 is always 1 and 𝑖 = √(−1) so i² = -1. 1 𝐱 -1 = -1.

π rounded to the nearest hundredth is 3.14, -1 𝐱 3.14 = -3.14.

So (-3.14) is the answer.

Why is the factorial of 0 = 1 ? What significance does it have if you find the number of permutations to arrange 0 items? Shouldn't it be 0?

Krishna Karthik - 1 year, 7 months ago

Basically the factorial of 𝐧 is 𝐧(𝐧-1)(𝐧-2)... all the way to 1

So the factorial of 5 is {5 𝐱 4 𝐱 3 𝐱 2 𝐱 1}

There is a pattern in factorials of all numbers:

{ 4! = 5!／5 = 24 }

{ 3! = 4!／4 = 6 }

{ 2! = 3!／3 = 2 }

{ 1! = 2!／2 = 1 }

SO { 0! = 1!／1 = 1 }

Meaning that 𝐧! =((𝐧-1)!) / {𝐧+1}

{This is the respond to Kao Cen Darach}

Prakash Kallanmarthodi - 1 year, 7 months ago