simplify e^{(1+i)z}

Solution

simplify

e^{(1 + i) z}

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

Solution steps

e^{(1 + i) z}

Apply imaginary number rule:

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

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

Rewrite

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

in standard complex form:

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

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

\frac{( x ^{2} - 14 x - 3 )}{( x ^{2} + 1 ) \cdot ( x - 3 )}

\frac{5 ( 3 + 3 )}{6}

\frac{7 x ^{2} - 2 x - 6}{( 2 x - 1 ) ( x ^{2} - 2 )}

\frac{z ^{2}}{( z ^{2} - z + 1 ) ( z + 1 )}

(1 + i, 2 - 3 i) (2 - i, - 1 + 2 i)