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Featured 4 months ago

(see below)

Based on the Pythagorean Theorem, we know that

#color(white)("XXX")a^2+b^2=c^2

Featured 4 months ago

Let us write the two complex numbers in polar coordinates and let them be

Here, if two complex numbers are

Their division leads us to

So for division complex number

Here

and

and

Hence,

Hence,

=

Featured 4 months ago

Given expression

Let

So

**Inserting**

Featured 3 months ago

Note first that as

Thus, the given problem is equivalent to the problem

Adding

Using the unit circle, we can tell that on our restricted interval, we have

Featured 3 months ago

You have to start by finding a point that lies on this line. I think the simplest would be

We now draw an imaginary triangle, as shown in the following diagram.

We can now clearly see that our side opposite

We must finally find the hypotenuse prior to determining the ratios. By pythagorean theorem:

However, the hypotenuse can never have a negative length, so we can only accept the positive solution. We can now find our ratios.

Hopefully this helps!

Featured 2 months ago

If

then

and

If

then

and

Plugging in the values for

If we call this value

then

and (since

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