Simplify (3 + 2i) + (1 - 5i)

Step by step

The question

Question: work out (3 + 2i) + (1 − 5i).

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 bracket with a plus or nothing in front can just be removed.

2 Group like parts

Like parts go together: the plain numbers are the real parts.

The parts with i go together too.

Real parts: 3 + 1 = 4.

i parts: 2i − 5i = −3i.

So the answer is 4 − 3i.

3 Check

Let's check: take away 1 − 5i.

We should get the first number again: 3 + 2i.

Let's look back.

First: open the brackets.

Then: group like parts.

Last: check.