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 Equivalent to ☺ 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) )
Common Errors – Some candidates thought thatis the same asand thatis the same as. – The “formula”for argumentsdoes not workfor points in the 2^{nd}and 3^{rd}quadrant. – Very many candidates seem unaware that their calculators will work in radians mode and there were many unnecessary “manual” conversions from degrees to radians. |