How to use the IMEXP() function in Excel

Its computes the exponential of a complex number, returning the result in rectangular form (x + yi). This is the complex analog of the standard EXP() function.

Syntax
IMEXP(complex_number)

Argument

• complex_number (required)
  A complex exponent in either:
  • « x+yi » format (mathematical convention)
  • « x+yj » format (engineering convention)

Technical Background
For a complex number z = x + yi:

IMEXP(z) = e^z = e^x · (cos y + i·sin y)

This implementation of Euler’s formula:

1. Separates into magnitude (eˣ) and phase (eⁱʸ) components
2. Converts the imaginary exponent using Euler’s identity

Example

=IMEXP(« 3-4i »)  // Returns « -13.1287831+15.2007845i »

Additional Examples

=IMEXP(« 1+i »)      // Returns « 1.46869394+2.28735529i »

=IMEXP(« 0+πi »)     // Returns « -1 » (Euler’s identity)

=IMEXP(« 2+0i »)     // Returns « 7.3890561 » (matches real EXP(2))

Key Features

• Maintains 8 decimal place precision
• Preserves input’s imaginary unit convention
• Handles all valid complex number formats
• Periodic in imaginary dimension (period 2π)

Error Conditions

• Returns #NUM! for:
  • Invalid complex number format
  • Non-numeric components
  • Missing imaginary unit when required

Usage Notes

1. For pure real numbers, equivalent to EXP()
2. For pure imaginary numbers, reduces to Euler’s formula
3. Essential for:
   • Complex differential equations
   • Fourier transforms
   • Quantum mechanical wavefunctions