Simplify (4 - i) - (2 + 3i)

Step by step

The question

Question: work out (4 − i) − (2 + 3i).

No real number times itself is negative.

So we use a new number: i, the square root of minus 1.

So i squared is minus 1.

1 Open the brackets

A minus in front of a bracket changes the sign of every part inside.

2 + 3i becomes −2 − 3i.

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 − 2 = 2.

i parts: −i − 3i = −4i.

So the answer is 2 − 4i.

3 Check

Let's check: add back 2 + 3i.

We should get the first number again: 4 − i.

Let's look back.

First: open the brackets.

Then: group like parts.

Last: check.