simplify e^{(1+i)t}

Solution

simplify

e^{(1 + i) t}

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

Solution steps

e^{(1 + i) t}

Apply imaginary number rule:

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

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

Rewrite

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

in standard complex form:

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

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

2 x (x - 2)

(a + h + a + h)^{2}

\frac{x ^{2} - 11 x + 6}{( x + 2 ) ( x ^{2} - 4 x + 4 )}

A (- 2, - 3) B (- 2, 3)

(s + 16 + 9 i) (s + 16 - 9 i)