Edexcel Further Maths Core Pure Year 1 | Complete Study Guide with Q&A

Edexcel Further Maths Core Pure
Year 1
i = - ANSWER>>√-1

Imaginary number - ANSWER>>A number of the form bi, where b ∈ R

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

Linking imaginary numbers to discriminant - ANSWER>>If b² - 4ac < 0, there are no real roots

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

You can multiply a real number by a complex number by - ANSWER>>multiplying out the
brackets in the usual way

If b² - 4ac < 0, then the quadratic equation ax² + bx + c has - ANSWER>>two distinct complex
roots, neither of which are real

i² = - ANSWER>>-1

Principal square root of a complex number - ANSWER>>√z, has a positive real part

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

z and z* are called - ANSWER>>a complex conjugate pair

You can use conjugates to - ANSWER>>divide two complex numbers

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

The complex number z = x + iy can be represented as - ANSWER>>the vector (x y) on an Argand
diagram

Modulus - ANSWER>>Magnitude of a corresponding vector

Modulus of a complex number - ANSWER>>|z|, distance from the origin to that number on an
Argand diagram.