Step by step
The question
Question: work out (4 + 3i) − (1 − 2i).
The numbers we know are called real numbers.
No real number times itself is negative.
3 times 3 is 9, and minus 3 times minus 3 is 9 too.
So we use a new number: i, the square root of minus 1.
A square root times itself gives back what is under it.
So i squared is minus 1.
There are four choices.
First we solve it, the normal way.
Then we pick.
1 Open the brackets
A minus in front of a bracket changes the sign of every part inside.
1 − 2i becomes −1 + 2i.
2 Group like parts
Like parts go together: the plain numbers are the real parts.
The parts with i go together too.
Real parts: 4 − 1 = 3.
i parts: 3i + 2i = 5i.
So the answer is 3 + 5i.
3 Check
Let's check: add back 1 − 2i.
We should get the first number again: 4 + 3i.
4 Pick the choice
Our answer is 3 + 5i.
That is choice B.
5 Why not the others
A is 3 + i.
Wrong: taking away −2i is adding 2i.
C is 5 + i.
Wrong: added the second bracket instead of taking it away.
D is 5 + 5i.
Wrong: added 1 instead of taking it away.
Let's look back.
First: open the brackets.
Then: group like parts.
Then: check.
Then: pick the choice.
Last: why not the others.