## 17Calculus Precalculus - Multiplying Complex Numbers

##### 17Calculus

Multiplying Complex Numbers

Multiplying works the same as with radicals. For example, let's multiply the same two numbers we used above, first with square root of 2 and then with complex numbers.
Example: $$(1+3\sqrt{2}) (6+8\sqrt{2}) = 1(6+8\sqrt{2}) + 3\sqrt{2}(6+8\sqrt{2}) =$$ $$6+8\sqrt{2} +18\sqrt{2} +24(2) =$$ $$54+26\sqrt{2}$$
Notice we had $$(\sqrt{2})^2 = 2$$.

Now lets multiply complex numbers. Example: $$(1+3i) (6+8i) = 1(6+8i) + 3i(6+8i) =$$ $$6+8i +18i +24i^2 =$$ $$6+26i - 24 = -18+26i$$
Notice that when we got $$i^2$$ and since $$i=\sqrt{-1}$$, this gives us $$i^2 = (\sqrt{-1})^2 = -1$$. So $$24i^2 = 24(-1)=-24$$.

Before we go on, let's watch a video to give us more information.

### Dr Chris Tisdell - Complex numbers are AWESOME [16min-46secs]

video by Dr Chris Tisdell

When using the material on this site, check with your instructor to see what they require. Their requirements come first, so make sure your notation and work follow their specifications.

DISCLAIMER - 17Calculus owners and contributors are not responsible for how the material, videos, practice problems, exams, links or anything on this site are used or how they affect the grades or projects of any individual or organization. We have worked, to the best of our ability, to ensure accurate and correct information on each page and solutions to practice problems and exams. However, we do not guarantee 100% accuracy. It is each individual's responsibility to verify correctness and to determine what different instructors and organizations expect. How each person chooses to use the material on this site is up to that person as well as the responsibility for how it impacts grades, projects and understanding of calculus, math or any other subject. In short, use this site wisely by questioning and verifying everything. If you see something that is incorrect, contact us right away so that we can correct it.