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Popular >

simplify e^{(2+i)t}

Solution

simplify

e^{(2 + i) t}

Solution

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

Solution steps

e^{(2 + i) t}

Apply imaginary number rule:

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

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

Rewrite

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

in standard complex form:

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

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

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Frequently Asked Questions (FAQ)

What is e^{(2+i)t} ?
The solution to e^{(2+i)t} is e^{2t}cos(t)+ie^{2t}sin(t)