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QUESTION: Dear Prof Scott

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

Awaiting your reply,

Thanks & Regards,

Prashant S Akerkar

ANSWER: Yes, it is possible, and it can also be in exponential notation.

Standard notation is 1.4E6 + i5.32E3 = 1,400,000 + 5,230i.

In exponential, we would have 1E6 + i1E6 = root(2)E6*cis(pi/2).

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

QUESTION: Dear Prof Scott

Thank you.

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 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

1. Using the method just described in the last answer, this can be done.

As the answers gets to a big difference between the real and complex parts, it acts just like when this is done with real numbers.

2. As was given I the last answer, the result is about as accurate as the real computations shown.

3. As far as exponentiation, it is known that e^(a+bi) = (e^a)(cos(b) + i*sin(a)).

This can be found in http://en.wikipedia.org/wiki/Complex_exponential_function#Complex_plane

in the section labeled, “Complex Plane”.

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Comment | Dear Prof Scott Thank you. Thanks & Regards, Prashant S Akerkar |

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