Simplify (9 + 3i)/3

Step by step, with the reason for every step · Dividing complex numbers · Algebra 2

Step by step

Question: work out (9 + 3i)/3.

9 + 3i3

Remember: i is the square root of minus 1.

So i squared is minus 1.

i = √(−1)

i² = −1

The bottom is a plain number: 3.

So each part on top is divided by it.

a + bc = ac + bc

9/3, and 3i/3.

= 93 + 3i3

9/3 is 3.

3/3 is 1.

So the answer is 3 + i.

= 3 + i

Let's check: times 3 undoes divided by 3.

We get 9 + 3i again.

It works!

Check: (3 + i) × 3 = 9 + 3i

Let's look back.

First: split the fraction.

Last: check.

Answer

= 3 + i

Try this one yourself, then check:

6 + 4i2

Show the answer

3 + 2i