100ei4

100ei4 is commonly read in mathematics as the complex number 100 e^{i4}, where i is the imaginary unit and e is Euler’s number. This compact notation uses Euler’s formula e^{i theta} = cos(theta) + i sin(theta). Applying this with theta = 4 radians yields 100 e^{i4} = 100 (cos 4 + i sin 4).

Numerically, cos(4) ≈ -0.653643620863612 and sin(4) ≈ -0.7568024953079282. Therefore, 100 e^{i4} ≈ -65.3643620863612 - 75.68024953079282 i.

In polar terms, the complex number has a magnitude (modulus) of 100 and an argument (angle) of 4 radians. This places the point on the circle of radius 100 in the complex plane at approximately 229.183 degrees from the positive real axis. It can also be written in rectangular form as a + bi with a ≈ -65.364 and b ≈ -75.680.

Usage of this form is common in complex analysis and signal processing, where exponential representations simplify multiplication and rotation of complex numbers. If "100ei4" is encountered outside this mathematical context, it may be a transcription variant or code; in standard mathematical usage, it denotes the complex number 100 e^{i4}.