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Geometry/Scientific Notation for Complex Numbers

Question
QUESTION: Dear Prof Azeem

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

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

Examples :

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

Thanks & Regards,
Prashant S Akerkar

It is possible to use scientific notation for either the real or imaginary part or both.  Scientific notation is just that: notation.  It does not matter what it is representing.  Any number can be represented in scientific notation, in theory.

Azeem

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

QUESTION: Dear Prof Azeem

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

1. 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.

2. 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 ?.

3. Is it possible also to compute for exponentiation where base and exponent are complex numbers

for example :

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

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

Thanks & Regards,
Prashant S Akerkar

Hi Prashant,

All the operations you mentioned can be performed using real or complex numbers written in scientific notation.  The justification is the same as above: scientific notation is merely a different way of writing the same number.

Regards,
Azeem
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Dear Prof Azeem Thank you. Thanks & Regards, Prashant S Akerkar

Geometry

Volunteer

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.

Publications
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.