Step by step
The question
Question: work out 2 over i.
Remember: i is the square root of minus 1.
So i squared is minus 1.
1 Multiply by the conjugate
The bottom has an i in it.
To remove it, we use the conjugate of i: the same number with the sign of the i part changed.
It is −i.
We multiply the top and the bottom by −i.
−i over −i is 1, so the value stays the same.
2 Multiply out
On top, times each part.
On the bottom too.
3 Change i² to −1
i² is minus 1.
So −i² change sign.
4 Group like parts
Real parts together, i parts together.
Top: −2i.
Bottom: 1, a plain number.
No i at the bottom now.
5 Split the fraction
Each part on top is divided by 1.
So the answer is −2i.
6 Check
Let's check: times i undoes divided by i.
Our top −2i times i is 2.
That is 1 times the question's top, 2, and the bottom is 1.
So the answer is right!
Let's look back.
First: multiply by the conjugate.
Then: multiply out.
Then: change i² to −1.
Then: group like parts.
Then: split the fraction.
Last: check.