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Further Mathematics
A Level

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 and an ...

JL
13989 Views

Find arsinh(x) in terms of x

let y=arsinh(x)x=sinh(y)=(ey - e-y)/22x=e- e-y2x*ey=ey-1 (multiply byey)0=(ey)2-2xey-1This i...

JB
8348 Views

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 ...

ZS
9591 Views

Find the inverse of the general 2x2 matrix A= ([a, b],[c, d]) when does this inverse exist?

This is a typical further maths question, doing it correctly is a matter of carrying out a two-step process. 

Start by finding the determinant of the matrix,

det(A)=ad-bc

LR
3414 Views

The curve C has polar equation 'r = 3a(1 + cos(x)). The tangent to C at point A is parallel to the initial line. Find the co-ordinates of A. 0<x<pi

Tangent is parallel, therefore (dy/dx)=0.

Find y:

y = r sin(x) = 3a(1 + cos(x))(sin(x))

Differentiate y with respect to x

dy/dx = 3a[(2cos(x) - 1...

SS
7147 Views

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