Simplify (6 + 5i) - (6 - 2i)

Step by step

The question

Question: work out (6 + 5i) − (6 − 2i).

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.

6 − 2i becomes −6 + 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: 6 − 6 = 0.

i parts: 5i + 2i = 7i.

So the answer is 7i.

3 Check

Let's check: add back 6 − 2i.

We should get the first number again: 6 + 5i.

Let's look back.

First: open the brackets.

Then: group like parts.

Last: check.