Imaginary & Complex Numbers - all wrapped up

Imaginary numbers are square roots of negative numbers like √(-1)

But we like to substitute the lowercase letter i for √(-1), so

√(-1)=i

Check out the following examples of imaginary numbers. You can rewrite the radicals using i.

√(-16)=√(-1)∙√16=i∙4=4i

√(-15)=√(-1)∙√15=i∙√15=i√15

√(-12)=√(-1)∙√12=i∙√(4∙3)=2∙i∙√3=2i√3

Now, complex numbers consist of imaginary AND real numbers. Most complex numbers have two terms. To keep things standard, mathematicians write the real part first and then the imaginary part: 3 + 2i. We like to say the general form for complex numbers is a + bi, where a and b are real numbers. (Remember! Real numbers can be rational or irrational. And real numbers are complex numbers but complex numbers are NOT real numbers – look at this example of a complex number: 5 – 0i.)

So, when you add and subtract complex numbers you have to combine like terms. We’ve done that before! Look at this example:

(7 + 3i) + (3 – i) = 7 + 3i + 3 - i = 10 + 2i

Now try this one:

(6 – 4i) – (8 + 2i)
= 6 – 4i – 8 – 2i = -2 - 6i

Assignment. Create an addition or a subtraction problem using complex numbers and post it and the solution on my blog!