COMPLEX NUMBERS. ARITHMETIC OPERATIONS WITH COMPLEX NUMBERS. Which complex representation is the best to use? It depends on the operation we want to perform. ADDITION.
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
Which complex representation is the best to use?
It depends on the operation we want to perform.
When performing addition/subtraction on two complex numbers, the rectangular form is the easiest to use. Addition of two complex numbers, C1 = R1 + jI1 and C2 = R2 + jI2, is merely the sum of the real parts plus j times the sum of the imaginary parts.
I1 - I2
R1 + R2
We can use the rectangular form to multiply two complex numbers
If we represent the two complex numbers in exponential form, the product takes a simpler form.
The complex conjugate of a complex number is obtained by merely changing the sign of the number’s imaginary part. If
then, C* is expressed as
Subtraction of two complex numbers, C1 = R1 + jI1 and C2 = R2 + jI2, is merely the sum of the real parts plus j times the sum of the imaginary parts.
The division of two complex numbers is also convenient using the exponential and magnitude and angle forms, such as
Although not nearly so handy, we can perform complex division in rectangular notation by multiplying the numerator and denominator by the complex conjugate of the denominator
A special form of division is the inverse, or reciprocal, of a complex number. If C = Mejq, its inverse is given by
In rectangular form, the inverse of C = R + jI is given by