H2 Maths: Complex Numbers 1 Page Notes
☺ When question involvespowers, multiplication or division, it may be helpful toconvert to exponential form.
☺ Please write Ƶ and 2 differently.
☺ De Moivre’s Theorem
Memory tip: Notice that arg behaves similarly to log.
☺ Locusof z is aset of pointssatisfying certain given conditions.
☺ in English means:The distance between (the point representing)and (the point representing)
☺ Means the distance offromis a constant,.
So this is acircular loci.
Centre:, radius =
☺ means that the distance offromis equal to its distance from
In other words, the locus is theperpendicular bisectorof the line segment joiningand.
☺ represents ahalf-linestarting frommaking an anglewith the positive Re-axis.
(Exclude the point (a,b) )
– Some candidates thought thatis the same asand thatis the same as.
– The “formula”for argumentsdoes not workfor points in the 2ndand 3rdquadrant.
– Very many candidates seem unaware that their calculators will work in radians mode and there were many unnecessary “manual” conversions from degrees to radians.