Note that even numbers are all divisible by 2. Examples are:

`2, 4 , 6 ,8 , 10, 12, 14, 16, 18, 20...`

Then, let's try to determine which of these even numbers would result to an odd quotient when divided by 2. Note that odd numbers are not divisible by 2.

`2-:2=1` `4-:2=2`

`6-:2=3` `8-:2=4`

`10-:2=5` `12-:2=6`

`14-:2=7` `16-:2=8`

`18-:2=9` `20-:2=10`

So, 2,6,10,14 and 18 are the even numbers that when divided by 2 result to odd numbers.

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**Therefore, **

** `2 + 4n` (where n is an integer)**

** are the even numbers that when divided by 2 result to an odd quotient.**

let n be any odd number then m = 2n is the number that when divided by 2 will give an odd number.

The series of numbers so obtained is 2*(1,3,5,7,9,11,-----)

or 2,6,10,14,18,22,----

this series is equivilant to:

**2+(4i) where i is an integer including zero**