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 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 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.

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