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===== Review of complex numbers (40 minutes) =====

Notes for representing harmonic motion, including complex numbers {{courses:lecture:oslec:reps_initcond_complexnumbers_wiki.ppt|}}

  * Whiteboard exercise: On a scale of 1 to 10, rate your knowledge of, and confidence using, complex numbers.

  * Introduce Argand plane, equivalence of $a+ib$ and $\left| r \right|e^{i\varphi }$ forms. Euler relation. Practice geometry: $a+ib$ is $a$ along $R_e$ axis and $b$ along $I_m$ axis OR $\left| r \right|$ rotated through angle $\varphi$ from $R_e$ axis.

  * Addition is easiest in rectangular form; multiplication in polar form.

  * Complex conjugate and modulus; rationalizing fractions.

  * Equating complex numbers gives $two$ pieces of information.

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