Math Is Fun Forum

Grader

Guest

Imaginary exponent

What is the value of e^i? Could you please explain

Bob

Administrator

Registered: 2010-06-20

Posts: 10,140

Re: Imaginary exponent

hi Grader,

Welcome to the forum.

In complex number theory a complex number, a number may be written

so your number will be

where this angle, 1,  is measured in radians.

Bob

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bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Imaginary exponent

Hi;

Welcome to the forum. Or you can derive it using Taylor series directly.

Now substitute i for x we get:

This can be separated as,

The first series on the RHS is cos(1) and the second series is i sin(1), so

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
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Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Imaginary exponent

Which, equivalently, can be expressed:

0.540... + i(0.841...)

Although, obviously, this is not nearly as neat

Last edited by Au101 (2012-08-20 01:37:12)

noelevans

Member

Registered: 2012-07-20

Posts: 236

Re: Imaginary exponent

Hi Grader!

Graphically this would be a point on the unit circle: one unit in the direction of positive 1rad or about 57.3 degrees.

Have a great day!

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Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).
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