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 def...
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
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