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Electrical Engineering/Scientific Notation for Complex Numbers.

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QUESTION: Dear Prof Cleggsan

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

1. 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.

Is it possible to also have a scientific notation for complex numbers ?.

Examples :


6720000000 + 4i
1991230000000 + 6i
18.7 + 2i


2. Can this also be taken as a valid example and written with scientific notations ?.

Here a & b are large numbers

6720000000 + 1991230000000i

Similarly example of small numbers

0.0000000000345 + 0.34562222222222i

i.e. a+bi complex form where a,b are real numbers.

3. The mathematical computations viz Multiplication, Division of two complex numbers where a & b for very large or very small numbers with use of scientific notation (10^9 OR E9) can become complex ?.

Awaiting your reply,

Thanks & Regards,
Prashant S Akerkar

ANSWER: I think you already answered your own question by listing the wiki web pages.

Scientific notation and complex numbers are basic math and used commonly in all engineering, scientific and tech fields of study.



---------- FOLLOW-UP ----------

QUESTION: Dear Prof Cleggsan

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

Is it possible also to compute exponentiation where base and exponent are both complex numbers ?.

For example :

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

Base = 6720000000 + 1991230000000i
Exponent = 0.0000000000345 + 0.34562222222222i

Awaiting your reply,

Thanks & Regards,
Prashant S Akerkar

Answer
I have not seen such in the literature and I don't know how to compute with such a number configuration.  

You can google for it but I did not find anyone treating that question in a couple of searches that I checked.  So, I am going to say that exponents must be rational whole or fractional numbers but not imaginary or complex numbers.

Let me know if you find out otherwise.

Here is a simplified explanation but not the full answer:

http://en.wikipedia.org/wiki/Exponentiation#Roots_of_arbitrary_complex_numbers  

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cleggsan

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All technical areas of Electronics Engineering.

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BSEE, MBA, Design, R&D, University Research.
Senior Life Member of IEEE. Life Fellow of AES.

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IEEE, Consumer Electronics Society, Audio Engineering Society.
Broad teaching experience; work experience mostly in consumer electronics and conversion from analog to digital technologies. Pioneer in digital audio at all levels.

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BSEE (Equiv) BYU BSEE University of North Dakota MSBA (MBA) Illinois State University Graduate Studies in Computer Science - Bradley University Graduate Studies - Ohio University Graduate Studies - University of Missouri Kansas City DeVry Tech - Electronics

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