﻿ Exponential to Rectangular Form Conversion Calculator ﻿ # Exponential to Rectangular Form Conversion Calculator

Formula Example Enter the Amplitude (r) Enter the Phase (θ) radians

This exponential to rectangular form conversion calculator converts a number in exponential form to its equivalent value in rectangular form.

Exponential forms of numbers take on the format, re, where r is the amplitude of the expression and θ is the phase of the expression. The amplitude r must be expressed in absolute value form. R cannot be a negative number. θ (theta) must be expressed in unit radians. Unlike the polar form, which is expressed in unit degrees, a complex exponential number is expressed in unit radians.

Rectangular forms of numbers take on the format, rectangular number= x + jy, where x and y are numbers. The x is the real number of the expression and the y represents the imaginary number of the expression.

Exponential forms of numbers can be converted into their rectangular equivalents by the following formulas. The real value (the x value) of the rectangular form can be obtained through the formula, x= r cos(θ). The imaginary value (the y value) of the rectangular form can be obtained through the formula, y= r sin(θ).

So, for example, let's take the expression in exponential form, 20ej1.95. We want to convert this into its equivalent rectangular form. So, to do this, we first obtain the x value. We take the formula and plug in the values, giving us, x= 20 cos(1.95)= -7.4. For the y value, we take the formula and plug in the values, giving us, y= 20 sin(1.95)= 18.58. So the rectangular form is then, -7.4 + j18.58.

And that's all that's required in order to convert from exponential form to the rectangular form.

Since the only 2 components of a number expressed in exponential form are the amplitude and the phase of the signal, these are the only 2 inputs required for the calculator to compute the equivalent number in rectangular form.

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