Euler's formula is .  It is remarkable in that it relates trigonometric function functions with complex numbers. Euler's formula maps the natural constant e raised to the complex exponent to the complex plane using the trigonometric expression . This equation is true only if the angle θ is measured in radians.
Click on the blue point in manipulative 1 and drag it to change the figure. The axes in manipulative 1 are the real axis and imaginary axis of the complex plane.
Euler's formula is named after Leonhard Euler who published it in its present form in 1748.
Leonard Euler was a very prolific mathematician. Note that the phrase Euler's Formula is used to indicate different formulas in different disciplines.
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