# Formula to Convert Complex Numbers from Polar to Rectangular Form in Excel(vice versa)

In this article, we will learn to convert complex numbers from rectangular to polar form and vice versa.

To convert the rectangular form to polar form, we need knowledge of the following theory of complex numbers:

## How to Create a complex Number in Excel:

In Excel, a complex number can be written using the **COMPLEX** function

`=COMPLEX(real_num, imag_num)`

Where

*real_num:** The complex numberâ€™s real coefficient. This argument is required.*

*imag_num:** The complex numberâ€™s imaginary coefficient. This argument is not required. The default value is zero if omitted.*

## Excel Function to Calculate Absolute or Magnitude of Complex Numbers

Magnitude of complex number can be found using the formula given below

`=IMABS(inumber)`

Where,

*inumber:**The complex number whose absolute value is to be returned*

## Excel Formula to Calculate Argument or Phase of Complex Numbers

Angle or phase of complex number can be determined using the following formula

`=IMARGUMENT(inumber)`

Where,

*inumber:**The complex number whose phase is to be returned*

## Excel Formula to Convert a Complex Number from Rectangular Form to Polar Form

Suppose a complex number is given in cell , Now we will convert it into polar form using the formula below

`=IMABS(B3)&"(cos "&IMARGUMENT(B3)&" + isin "&IMARGUMENT(B3)&")"`

**IMARGUMENT**function returns the phase of the complex number in radians, we will inject the**DEGREES**function to convert radians to degree

`=IMABS(B3)&"(cos "&DEGREES(IMARGUMENT(B3))&" + isin "&DEGREES(IMARGUMENT(B3))&")"`

- To limit the precision, we will apply the
**ROUND**function. and a degree symbol is added for a better look. Ampersand (&) is added to concentrate all text values.

`=ROUND(IMABS(B3),2)&"(cos "&ROUND(DEGREES(IMARGUMENT(B3)),2)&"Â°"&" + isin "&ROUND(DEGREES(IMARGUMENT(B3)),2)&"Â°)"`

## Excel Formula to Convert a Complex Number From Polar to Rectangular Form

To convert a complex number from polar to rectangular form we have to determine the following parts of the rectangular form

**X = r.cos(Î¸)**

**Y = r.sin(Î¸)**

In Excel, we can apply the following formulas to obtain our purposes:

- To calculate the value of X

`=ROUND(COS(RADIANS(MID(B3,10,4)))*LEFT(B3,4),0)`

- To calculate the value of Y

`=ROUND(SIN(RADIANS(MID(B3,24,5)))*LEFT(B3,4),0)`

**Explanation(for Y):**

**MID(B3,24,5):**retrieves a substring of five characters from cell**B3**, beginning at character 24.**RADIANS(MID(B3,24,5)):**Angles are converted from degrees to radians using the**RADIANS**function.- The formula
**SIN(RADIANS(MID(B3,24,5)))**determines the sine of the obtained angle in radians. - From cell
**B3**â€˜s leftmost four characters,**LEFT(B3,4)**extracts them (which implies the value of magnitude**r**). Then multiplied with the**SIN(RADIANS(MID(B3,24,5)))** - The result is rounded to the nearest whole number using the formula
**ROUND(SIN(RADIANS(MID(B3,24,5)))*LEFT(B3,4),0)**.

A similar, explanation is also applied for the formula to obtain the value of** X**

Then Just Apply the **COMPLEX **Function as Below

`=COMPLEX(C3,D3,"i")`