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Geometry/Complex Number Variant.

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Question
Dear Prof Azeem

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
Hi Prashant,

How the number is plotted on the graph has no bearing on the number itself.  Operations on complex numbers will be completely untouched.

Really, all this does is induce a reflection on all complex graphs.  This reflection must be carried over in any application of the complex numbers.

Ultimately, this is a matter of convention.  Neither way offers an advantage.


Thanks for asking,
Azeem

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Azeem Hussain

Expertise

I welcome your questions on algebra, 2D and 3D geometry, parabolic functions and conic sections, and any other mathematical queries you may have.

Experience

4 years as a drop-in and by-appointment tutor at Champlain College. Private tutor for dozens of clients over the past 8 years.

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CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry

Education/Credentials
Bachelor of Science, Major Mathematics and Major Economics, McGill University, 2014. Diploma of Collegiate Studies; Pure and Applied Science, Champlain College Saint-Lambert, 2010.

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