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Further Mathematics

A Level

The set of midpoints of the parallel chords of an ellipse with gradient, constant 'm', lie on a straight line: find its equation; equation of ellipse: x^2 + 4y^2 = 4

// Allow me to make the question more explicit: we have a set of lines of equal gradients ‘m’. We need to find a line through which the midpoints of the intersections of these lines with the ellipse; a...

Answered by Drew P. • Further Mathematics tutor

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Prove by induction that n^3+5n is divisible by 3 for every natural number.

Proof by induction has three core elements to it. To start with you must prove that the statement is true for the 'basic case'. For the most part this is 1, but some questions state it is higher.

Answered by Philip D. • Further Mathematics tutor

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Find the square root of i

When dealing with powers of complex numbers, always start by putting the quantity into exponential form.

i has a magnitude of 1 and an ...

Answered by Jamie L. • Further Mathematics tutor

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Find arsinh(x) in terms of x

let y=arsinh(x)x=sinh(y)=(e^y - e^-y)/22x=e^y- e^-y2x*e^y=e^y-1 (multiply bye^y)0=(e^y)²-2xe^y-1This i...

Answered by Joe B. • Further Mathematics tutor

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write 2-2i in its modulus argument form

firsly sketch out the 2-2i on an argand diagrm and draw a line from (0,0) to (2,-2). With the shortest distance Mark the angle theta from the positive x-axis to the line to see whether the argument is ...

Answered by Zivanayi S. • Further Mathematics tutor

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