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# Electrical Engineering/Scientific Notation for Complex Numbers.

Question
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 ?.

Thanks & Regards,
Prashant S Akerkar

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

Thanks & Regards,
Prashant S Akerkar

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

Electrical Engineering

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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.
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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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