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Firstly, we note that z being a complex number can be expressed in the form z = a + bi. If we then take the complex conjugate of this expression, the real numbers remain the same (as they are their own c con...

Let me rephrase this question slightly: "Find all the roots of the equation x^n - 1 = 0." We know by the fundamental theorem of algebra that an nth degree polynomial has exactly n roots. So the exc...

Say you have a differential equation of the form: dy/dx + Py = Q , where P and Q are functions of x. Remember that even if your equation doesn't initially look like this, you may be able to rearrange it into...

The asymptotes of a curve are the lines or curves that approach a given curve very closely without actually touching it. They make curve sketching much easier. You will probably only have asymptotes that are...

Let's begin by reviewing a fairly simple (linear) equation: (1) y = 2x + 3 (1) describes the relationship between two variables, x and y . Given a value for one, we can use (1) to work out the value of the u...