Name: Adding complex numbers: solution walkthrough
Uploaded: 2026-11-13
Duration: 1 min 30 s
Description: For the complex numbers z = 3 + 2i and w = 1 - 5i, what is 2z + w? Try it, then watch the animated solution.

A complex number has a real part and an imaginary part. Draw

z = 3 + 2i

as an arrow:

3

across,

2

up.

Multiply both parts of

z

by

2

:

2(3 + 2i) = 6 + 4i

.

Now add

w = 1 - 5i

. From the tip of

2z

, go

1

across and

5

down.

Add real parts with real parts and imaginary with imaginary:

6 + 1 = 7

and

4i - 5i = {-i}

.

Traps:

4 - 3i

forgets the

2

,

7 + 9i

adds the

5i

, and

7 - 3i

doubles only the real part.

Try it first