simplify e^{(1+i)x}

Solution

simplify

e^{(1 + i) x}

e^{x} cos (x) + i e^{x} sin (x)

Solution steps

e^{(1 + i) x}

Apply imaginary number rule:

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

= e^{x} (cos (x) + i sin (x))

Rewrite

e^{x} (cos (x) + sin (x) i)

in standard complex form:

e^{x} cos (x) + e^{x} sin (x) i

= e^{x} cos (x) + e^{x} sin (x) i

u (6, - 4, - 2) v (5, 3, 4)

(vx - 2 x) (v d x + x d v)

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