Edexcel Further Maths Core Pure Year 1 exam questions with well verified answers

Edexcel Further Maths Core Pure Year 1
i = - correct answer √-1



Imaginary number - correct answer A number of the form bi, where b ∈ R



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



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



Complex numbers can be added or subtracted by - correct 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 - correct answer multiplying out the brackets in
the usual way



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



i² = - correct answer -1



Principal square root of a complex number - correct answer √z, has a positive real part



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



z and z* are called - correct answer a complex conjugate pair



You can use conjugates to - correct answer divide two complex numbers



Argand diagram - correct answer - Represents complex numbers

- x-axis is the real axis and y-axis is the imaginary axis

, Edexcel Further Maths Core Pure Year 1
- 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 - correct answer the vector (x y) on an Argand
diagram



Modulus - correct answer Magnitude of a corresponding vector



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



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



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



The argument of a complex number, arg z, is - correct answer the angle between the positive real axis
and the line joining that number to the origin on an Argand diagram, measured in an anti clockwise
direction



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



Principal argument - correct answer The argument Theta of any complex number is usually given in the
range -pi < theta < pi



Let a be the positive angle made with the real axis by joining the origin and z. If z lies in the first quadrant
then - correct answer arg z = a



Let a be the positive angle made with the real axis by joining the origin and z. If z lies in the second
quadrant then - correct answer arg z = pi - a



Let a be the positive angle made with the real axis by joining the origin and z. If z lies in the third
quadrant then - correct answer arg z = -(pi - a)