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Calculus/Complex Number Variant.

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Question
Dear Prof Abe

http://en.wikipedia.org/wiki/Complex_number

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, where i2 = −1. In this expression, a is the real part and b is the imaginary part of the complex number. Complex numbers extend the concept of the one-dimensional number line to the two-dimensional complex plane by using the horizontal axis for the real part and the vertical axis for the imaginary part. The complex number a + bi can be identified with the point (a, b) in the complex plane.


1. Can this be also considered as a variant of Complex Number where the vertical axis Y is used for the real part and the horizontal axis for the imaginary part ?.
i.e. The complex number ai + b can be identified with the point (a, b) in the complex plane. The complex plane will be the x -axis
instead of the conventional y-axis. a and b are real numbers, only the real and imaginary coefficients are interchanged with the axis.

Examples : 2i+3 , 4i-5, -3i+6 etc

The complex variant conjugate for example 4i + 9 will be -4i+9

The plotting of the complex numbers variant will also vary since the complex plane is taken as the x-axis.

2. In this case for the complex number variant, the complex number arithmetic viz multiplication, subtraction, division, addition , exponentiation etc will also be impacted ?.

4. Do you feel this complex number variant can be also considered in math applications viz control theory, geometry, electricl engineering etc ?.


Awaiting your reply,

Thanks & Regards,
Prashant S Akerkar

Answer
Hello Prashant,

In answer to your questions:
1. Sure, it can work just fine if you switch the real & imaginary axes.
.  Just a matter of convention.

2. Yes, the plotting of such will of course have to change to match the
.  designation of the real & imaginary axes...but the results will naturally
. be consistent.

4. Yes, same as it is now.

Abe

Calculus

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Abe Mantell

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Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

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Over 15 years teaching at the college level.

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B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook

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