Mathematics: Applications and Interpretation · Topic 1: Number and algebra

AHL1.13 — Complex numbers: polar and exponential form

Mathematics: Applications and Interpretation · SL / HL · syllabus-mapped notes

1. AIAHL1.13.1

   Polar and exponential (Euler) form

   $z=r\,\mathrm{cis}\,\theta=r\mathrm{e}^{i\theta}$; converting between Cartesian, polar and exponential.

2. AIAHL1.13.2

   Products, quotients, powers and geometry

   Multiplying rotates and stretches; adding/subtracting is vector addition.

3. AIAHL1.13.3

   Application: AC circuits and adding sinusoids

   Voltages as complex quantities; combining sinusoids of the same frequency.