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Advanced Math/Complex Number Data in Excel Application.

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Question
Dear Prof Scott

http://en.wikipedia.org/wiki/Microsoft_Excel‎
http://office.microsoft.com/en-us/excel/
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.

Examples
---------

6720000000 + 4i

1991230000000 + 6i

18.7 + 2i

6720000000 + 1991230000000i

0.0000000000345 - 0.34562222222222i


1. Do the current excel version allows us to enter complex number data in cells ?.

Data supported are : Number,Currency, Date, Time, Percentage, Fraction, Scientific,Text, Special,Custom

2. Can it be useful to enter Complex Number Data in Excel Spreadsheet ?.

3. Functions, Formulas in Excel can then be used for adding, subtracting,multiplication,division,power etc
of complex numbers ?.

Examples : SUM(), POWER(),PRODUCT() etc

Awaiting your reply,

Thanks & Regards,
Prashant S Akerkar

Answer
1. No, the current version of Excel as is can't enter complex numbers, but a sheet to do operations on them could be created by using two cells for each number.

Let x = 2 + 3i and y = 4  + 5i.  Put x in row 1 and y in row 2 as follows:
Put 2 in A1 and 3 in B1 for x
Put 4 in A2 and 5 in B2 for y.

For the sum, in A4 put =A1+A2 and in B4 put =B1+B2.
This should give 6 in A4 (the real part) and 8 in B4 (the imaginary part).

For the product, in A6, put =A1*A2-B1*B2 and
in B6, put =A1*B2+B1*A2.
This should give -7 in A6 (the real part) and 22 in B6 (the imaginary part).

The results would be changed by altering the numbers in A1, A2, B1, and B2.

2. Yes, it can be very useful.
By the way, formula could be put in the change from rectangular
coordinates (x,y) to polar coordinates (r,A).
That is, r = sqrt(x + y) and tan(A) = y/x.

3. I have just shown addition and multiplication.
Subtraction could be done by entering
=A1-A2 in A5 and =B1-B2 in B5 (right between addition and multiplication.

For division

This is taken from http://en.wikipedia.org/wiki/Complex_number.

Back to the spreadsheet, we would have a in A1, b in B1, c in A2, and d in B2.

So using cells A7, put in =(A1*A2+B1*B2)/sqrt(A2^2+B2^2) and in
A8 put =(B1*A2-A1*B2)/sqrt(A2^2+B2^2).

In summary, it can be done, but each complex number takes two cells.  

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Scott A Wilson

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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?

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Experience in the area; I have tutored people in the above areas of mathematics for over two years in AllExperts.com. 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.

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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.

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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.

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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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