Edexcel Further Maths Core Pure Year 1

Edexcel Further Maths Core Pure Year 1
(nΣr=1) (f(r) + g(r)) = - answer-(nΣr=1) f(r) + (nΣr=1) g(r)

(nΣr=1) kf(r) = - answer-k(nΣr=1) f(r)

Argand diagram - answer-- Represents complex numbers
- x-axis is the real axis and y-axis is the imaginary axis
- z = x + iy is represented by the point P(x,y) where x and y are Cartesian coordinates

Argument of a complex number - answer-the angle its corresponding vector makes with the
positive real axis

Complex number - answer-Written in the form a + bi, where a, b ∈ R

Complex numbers can be added or subtracted by - answer-adding or subtracting their real parts
and adding or subtracting their imaginary parts

For a complex number z = x + iy, the modulus is given by - answer-|z| = root(x² + y²)

For a complex number z =x + iy, the argument theta satisfies - answer-tantheta = y/x

For a complex number z with |z| = r and arg(z) = theta, the modulus-argument form of z is -
answer-z = r(cos(theta) + isin(theta))

For any complex number z = a + bi, the complex conjugate of the number is defined as -
answer-z* = a - bi

For any two complex numbers z1 and z1, arg(z1z2) = - answer-arg(z1) + arg(z2)

For any two complex numbers z1 and z2, |z1/z2| = - answer-|z1|/|z2|

For any two complex numbers z1 and z2, arg(z1/z2) = - answer-arg(z1) - arg(z2)

For any two complex numbers z1 and z2' |z1z2| = - answer-|z1||z2|

For two complex numbers z1 = x1 + iy1 and z2 = x2 + iy2, |z2 - z1| represents - answer-the
distance between the points z1 and z2 on an Argand diagram

Given z1 = x1 + iy1, and z2 = x2 + iy2, the locus of points z on an Argand diagram such that |z -
z1| = |z - z2| is - answer-the perpendicular bisector of the line segment joining z1 and z2

Given z1 = x1 + iy1, the locus of point z on an Argand diagram such that |z - z1| = r, or |z - (x1 +
iy1)|, is - answer-a circle with centre (x1,y1) and radius r.

Given z1 = x1 + iy1, the locus of points z on an Argand diagram such that arg(z - z1) = theta is -
answer-a half line from, but not including, the fixed point z1, making an angle theta with a line
from the fixed point z1 parallel to the real axis

half line - answer-A straight line extending from a point infinitely in one direction only