Question commentary

Question	Inspired by	Contents
Qn 1302	-	Complex numbers in cartesian form: multiplication, division and exponentiation linear and quadratic equations
Qn 1301	2007 P1 Q3b	Equality of complex numbers: solving an equation with complex roots by comparing real and imaginary parts
Qn 1303	-	Complex roots of a polynomial equation: conjugate roots when the coefficients are real quadratic equation with complex coefficients
Qn 1304	-	Complex numbers in polar form: conversions between cartesian and polar forms multiplication, division, exponentiation and conjugation in polar form conditions for a complex number to be real/purely imaginary
Qn 1305	2012 P1Q6	Complex numbers in both cartesian and polar form: conditions for a complex number to be real/purely imaginary (cartesian form) properties of $\|z^n\|$ and $\textrm{arg}(z^n)$ representation of complex numbers in the Argand diagram

Notable concepts that are missing from our collection of questions include:

Quadratic factors arising from complex conjugate roots (as seen in the 2007 paper)
Complex square roots stemming from a hint (as seen in the 2011 paper)
use of the "half angle trick" (as seen in the 2019 as well as 2017 specimen paper)
simultaneous equations (as seen in the 2017 specimen paper)

TYS analysis

Year	Question	Math Atlas	Comments
2007	P1 Q3b	Qn 1301	Qn 1301 is directly inspired by this question
2007	P1 Q7i	-	Not implemented: obtaining quadratic factor due to conjugate roots
2008	P1 Q8	Qn 1302 Qn 1303 Qn 1305	Complex arithmetic, cubic equation, Argand diagram
2008	P2 Q3a	Qn 1304	Polar form: conditions to be real
2009	-	-	Out of syllabus
2010	P1 Q8	Qn 1304	Complex arithmetic in polar form
2010	P2 Q1	Qn 1302 Qn 1303	Quadratic equation, quartic equation
2011	P1 Q10	-	Planned future implementation: extension of comparing real and imaginary parts and use of the quadratic formula
2012	P1 Q6	Qn 1305	Qn 1305 is directly inspired by this question
2013	P1 Q4	Qn 1302 Qn 1303	Complex arithmetic, cubic equation
2013	P1 Q8	Qn 1304	Polar form arithmetic
2014	P1 Q5	Qn 1305	Extension of concepts covered in Qn 1305 (conditions for complex number in cartesian form to be real)
2014	P2 Q4b	Qn 1304	Polar form arithmetic, conditions to be real
2015	P1 Q9a	Qn 1305	Cartesian form: conditions to be purely imaginary
2016	P1 Q7	Qn 1302 Qn 1303	Quadratic equation, cubic equation
2017	Specimen P1 Q7	-	Planned future implementation: simultaneous equations and the "half-angle trick"
2017	P1 Q8	Qn 1302 Qn 1303	Quadratic equation, quartic equation
2018	P2 Q2	Qn 1303 Qn 1305	Quartic equation, cubic equation, Argand diagram
2019	P1 Q1	Qn 1303	Cubic equation
2019	P1 Q9	-	Planned future implementation: use of the "half-angle trick" Video solution/discusssion on Youtube.
2020	P1 Q4	Qn 1304	Polar form: arithmetic and conditions to be purely imaginary
2020	P1 Q6	Qn 1303	Quadratic equations with complex coefficients