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Advanced Math/Scientific Notation for Representing Complex Numbers.


QUESTION: Dear Prof Scott

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 ?.


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

For example :

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
in the section labeled, “Complex Plane”.

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Scott A Wilson


I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can also say that I broke 5 minutes for a mile, which is over 12 mph, but is that relevant?


Experience in the area; I have tutored people in the above areas of mathematics for over two years in I have tutored people here and there in mathematics since before I received a BS degree back in 1984. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

Awards and Honors
I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

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My clients have been students at OSU, people who live nearby, friends with math questions, and several people every day on the PC. I would guess that you are probably going to be one more.

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