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#Engineering

IMEXP

Excel Functions

Get exponential of complex number.

Syntax

EXCEL 
=IMEXP(complex_num)

Arguments

Parameter Description
complex_num The complex number in the form "x+yi".

Return Value

Returns the exponential of a complex number.

Details

The Excel IMEXP function returns the exponential of a complex number. For example, given "0+πi" as input, the function returns "-1+3.23108914886517E-15i" as output. The output is essentially -1, but due to floating point precision, it contains a very small imaginary component. Given real number input, the function behaves like the exponential function and models exponential growth. Given imaginary input representing an angle, the function returns the corresponding point on the unit circle in the complex plane. The complex exponential function often appears as the Latin letter e to some power. This notation is equivalent to passing the complex number as input to the exponential function. In Excel, we write the exponential of a complex number "z=x+yi" like this:

Examples

Example 1

The Excel IMEXP function returns the exponential of a complex number. For example, given "0+πi" as input, the function returns "-1+3.23108914886517E-1

EXCEL 
=IMEXP(COMPLEX(0,PI())) // returns -1 + 3.23108914886517E-15i
Example 2

Given real number input, the function behaves like the exponential function and models exponential growth.

EXCEL 
=IMEXP(COMPLEX(1,0)) // returns 2.71828182845905
Example 3

Given imaginary input representing an angle, the function returns the corresponding point on the unit circle in the complex plane.

EXCEL 
=IMEXP(COMPLEX(0,PI()/3)) // returns cos(π/3) + sin(π/3)i
Notation

In Excel, we write the exponential of a complex number "z=x+yi" like this:

EXCEL 
=IMEXP(COMPLEX(x,y))
Euler's Formula

In Excel, we can see this behavior in the following formula:

EXCEL 
=IMEXP(COMPLEX(0,PI()/3)) // returns 0.5 + 0.866025404i
Explanation

In Excel, the complex exponential function is equivalent to this formula.

EXCEL 
=IMPRODUCT(
    COMPLEX(EXP(x), 0),
    COMPLEX(COS(y), SIN(y))
)

See Also

COMPLEX IMLN