Mr. Integral
Math notes/Linear Algebra/Eigenvalues and Dynamics

Complex Numbers and Oscillatory Modes — Cheat sheet

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Core rule

i2=−1,∣a+ib∣=a2+b2,(reiθ)k=rkeikθ.i^2=-1,\quad |a+ib|=\sqrt{a^2+b^2},\quad (re^{i\theta})^k=r^ke^{ik\theta}.

Watch for

Real matrices may require complex eigenvectors. For complex inner products, use conjugate transpose.