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Where z is a complex number, what is the cartesian form of |Z-2+3i| = 1?

Z is simply a general complex number, which can be written as Z = x+iyHere |Z-2+3i| = 1 can be written as |Z-(2-3i)| = 1, which is just an expression for every Z whose distance from the point (2,-3i) is equa...
MH
Answered by Mark H. • Maths tutor
10863 Views

Find the integral of log|x| by integration by parts

The question says to use integration by parts on this question, but at the minute we only have one variable. Therefore, we introduce a 1, so that log|x|= 1*log|x|, here we have not altered the value of the f...
LP
Answered by Laura P. • Maths tutor
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Show that the derivative of ln(x) = 1/x

We can start by letting y = ln(x) What we are trying to show is that dy/dx = 1/x Since y = ln(x), then e y = e ln(x) = x Taking the derivative of each side of this equation will give us e y .dy/dx = 1 If we ...
JC
Answered by James C. • Maths tutor
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Differentiate y = x^3 +x^2 - 4x +5 with respects to x.

When differentiating, you want to use the formula ax^n differentiates to (a n)x^(n-1), so for the example above, x^3 where a is 1, and n is 3, the differentiation is (1 3)x^(3-1) which results to 3x^2. This ...
MS
Answered by Manojhan S. • Maths tutor
4802 Views

Solve the differential equation: e^(2y) * (dy/dx) + tan(x) = 0, given that y = 0 when x = 0. Give your answer in the form y = f(x).

This is a question taken from a core 4 paper and is a typical example of a differential equation question. The first thing to notice about this equation is that it is "separable", meaning we can re...
DD
Answered by Dominic D. • Maths tutor
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