# H2 Maths Tuition: Complex Numbers Notes

H2 Maths: Complex Numbers 1 Page Notes

 Modulus Argument Cartesian Form  Draw diagram first, then find the appropriate quadrant and use (can use GC to double check) Polar Form   Exponential Form    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 of from is a constant, .

So this is acircular loci.

Centre: , radius =   means that the distance of from is equal to its distance from In other words, the locus is theperpendicular bisectorof the line segment joining and .  represents ahalf-linestarting from making an angle with the positive Re-axis.

(Exclude the point (a,b) ) Common Errors

– Some candidates thought that is the same as and that is 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. ## Author: mathtuition88

http://mathtuition88.com

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