Complex numbers, Imaginary axis, Imaginary unit, Algebraic form, Addition, Multiplication, Complex conjugate, Division.
Here is this thing… well, a polynomial. Let’s try to turn it into a product of linear factors.
Here comes this formula:
And now let’s try to factorize this one:
There is no such identity as
so we try using the previous one, with some hocus-pocus.
Next, let's see a more complicated one.
One significant benefit of complex numbers is that using complex numbers, all polynomials can be factored into linear factors.
This is called the Fundamental Theorem of Algebra.
Now, let’ solve some quadratic equations that we thought were hopeless.
Here comes the solution formula:
The absolute value of a complex number is its distance from zero.
We can compute this distance using the Pythagorean Theorem.
Let's see one more.
Instead of the formula, here we try factorization.
And now let’s see what else we can do with these complex numbers.