Question

Differential equations: Turn exp(-1+2i) into sines and cosines. Thanks!

Answer 1

Use Euler's formula:\[\exp((a+ib)x)=\exp(ax)\exp(ibx)=\exp(ax)(\cos(bx)+i\sin(bx))\]
Or, as it's more commonly written,
\[\large e^{(a+ib)x}=e^{ax}e^{ibx}=e^{ax}\left(\cos(bx)+i\sin(bx)\right)\]