Complex Number Worksheets

Examples, solutions, videos, and worksheets to help Algebra II students learn how to multiply complex numbers.

How to multiply complex numbers?

There are three sets of multiply complex numbers worksheets

In mathematics, the imaginary unit i is defined as the square root of -1. It is a fundamental concept in complex numbers. Powers of i repeat in a cyclic pattern, which makes them predictable. Here are the powers of i up to i 5 :

  1. i 1 = i
  2. i 2 = -1 (since i is square root of -1)
  3. i 3 = -i (since i 3 is the product of i 2 and i)
  4. i 4 = 1 (since i 4 is the square of -1)
  5. i 5 = i (since i 5 is the product of i 4 and i) The pattern repeats from i 5 . i 6 = i 2 and so on.

Multiply binomial complex numbers
To multiply binomial complex numbers, you use the distributive property of multiplication over addition.

Here’s how you multiply two complex numbers (a + bi) and (c + di)

Distribute each term in the first binomial to each term in the second binomial:
(a + bi) · (c + di)
= a · c + a · di + c · bi + bi · di
= ac + adi + bci + bdi 2
= ac + adi + bci - bd
= ac - bd + (ad + bc)i

Example:
Multiply (2 + 3i) by (1 − 4i):

Use the distributive property to multiply the terms:
(2 + 3i) · (1 − 4i)
= (2 · 1) + (2 · -4i) + (3i · 1) + (3i · - 4i)
= 2 - 8i + 3i - 12i 2
= 2 - 5i - (-12)
= 14 - 5i

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Complex Number Worksheet

More Complex Number Worksheets

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