Covered in AA HL and AI HL, the treatment of complex numbers is extended to modulus-argument (polar) form and Euler's form. Students convert between Cartesian, polar and Euler representations and perform products, quotients and powers in these forms. In AA HL, De Moivre's theorem is introduced and applied to find powers and roots of complex numbers, with proof by induction for the case n ∈ ℤ⁺. In AI HL the focus is on geometric interpretation and applications such as adding sinusoidal functions with the same frequency but different phase shifts.
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Video lessons
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