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Popular >

simplify e^{2x+i2y}

Solution

simplify

e^{2 x + i 2 y}

Solution

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

Solution steps

e^{2 x + i 2 y}

Apply imaginary number rule:

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

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

Rewrite

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

in standard complex form:

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

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

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Frequently Asked Questions (FAQ)

What is e^{2x+i2y} ?
The solution to e^{2x+i2y} is e^{2x}cos(2y)+ie^{2x}sin(2y)