What is e^{2(x+yi)+i} ?

The solution to e^{2(x+yi)+i} is e^{2x}cos(1+2y)+ie^{2x}sin(1+2y)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify e^{2(x+yi)+i}

simplify

e^{2 (x + y i) + i}

e^{2 x} cos (1 + 2 y) + i e^{2 x} sin (1 + 2 y)

Solution steps

e^{2 (x + y i) + i}

Apply imaginary number rule:

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

= e^{2 x} (cos (2 y + 1) + i sin (2 y + 1))

Rewrite

e^{2 x} (cos (2 y + 1) + sin (2 y + 1) i)

in standard complex form:

e^{2 x} cos (2 y + 1) + e^{2 x} sin (2 y + 1) i

= e^{2 x} cos (2 y + 1) + e^{2 x} sin (2 y + 1) i

\frac{( x + 1 ) ^{10}}{( 4 x - 8 ) ^{11}}

\frac{( s + 1 )}{( s + 2 ) ^{3} ( s + 3 )}

e^{i (θ + x)}

(1 + 3 x^{2} - 2 x^{4})^{6}

\frac{x ( x - 10 )}{2}

What is e^{2(x+yi)+i} ?
The solution to e^{2(x+yi)+i} is e^{2x}cos(1+2y)+ie^{2x}sin(1+2y)