What is e^{(1+2i)t} ?

The solution to e^{(1+2i)t} is e^tcos(2t)+ie^tsin(2t)

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simplify e^{(1+2i)t}

simplify

e^{(1 + 2 i) t}

e^{t} cos (2 t) + i e^{t} sin (2 t)

Solution steps

e^{(1 + 2 i) t}

Apply imaginary number rule:

e^{a + ib} = e^{a} (cos (b) + i sin (b))

= e^{t} (cos (2 t) + i sin (2 t))

Rewrite

e^{t} (cos (2 t) + sin (2 t) i)

in standard complex form:

e^{t} cos (2 t) + e^{t} sin (2 t) i

= e^{t} cos (2 t) + e^{t} sin (2 t) i

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