Solved Problems for Complex Numbers (Multivariable Calculus)

In summary, for those in need of solved problems for complex numbers in multivariable calculus, there are several helpful websites such as exampleproblems.com, math.berkeley.edu, and webmath.com. These sites offer sample problems, solutions, and past exams for practice. Some recommended resources include the Calculus book by Edwards and Penney and the course archive on math.berkeley.edu. Webmath.com is also suggested as a useful site for solving problems.
  • #1
kring_c14
76
0
need sites for solved problem pls...

anyone know a website that has solved problems for complex numbers (multivariable calculus)? my finals is on Monday and there aren't enough sample problems in our book, some are very basic.. i really need help..
 
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  • #2
pls pls pls...
 
  • #3
do as much homework as you can! try the even problems too. btw, what book and do you have the soln manual to it?
 
  • #4
calculus by edwards and penney..its more on integral and differential calculus. it only has introduction to complex numbers.. more on vectors and stuff like that... i can't find any sample problems like finding the principal values..
 
  • #6
thanks for the site.. its a great help
 
  • #7
math.berkeley.edu has a course archive - many of the course websites have assigned problem sets with solutions and or sample or real exams with solutions. I just completed a course in the theory of complex functions and I found the course archive to be a great help. They also archive old exams but these do not have solutions but are great anyways.

Cheers,
Siddharth M
 
  • #8
great site..thank you..
 
  • #9
example problem is an awesome site
 
  • #10

Related to Solved Problems for Complex Numbers (Multivariable Calculus)

1. What are complex numbers?

Complex numbers are numbers that contain both a real and imaginary component. They are written in the form a + bi, where a represents the real component and bi represents the imaginary component. Complex numbers are often used in fields such as engineering, physics, and mathematics to represent quantities that cannot be expressed solely with real numbers.

2. How are complex numbers added and subtracted?

To add or subtract complex numbers, you simply combine the real components and the imaginary components separately. For example, (3 + 4i) + (2 + 6i) = (3 + 2) + (4i + 6i) = 5 + 10i. Similarly, to subtract, you subtract the real components and the imaginary components separately. For example, (5 + 8i) - (3 + 2i) = (5 - 3) + (8i - 2i) = 2 + 6i.

3. How are complex numbers multiplied and divided?

To multiply complex numbers, you use the FOIL method (First, Outer, Inner, Last). For example, (2 + 3i)(4 + 5i) = (2)(4) + (2)(5i) + (3i)(4) + (3i)(5i) = 8 + 10i + 12i + 15i^2 = -7 + 22i. To divide complex numbers, you use the conjugate of the denominator to eliminate the imaginary component from the denominator. For example, (3 + 2i) / (2 - 5i) = (3 + 2i)(2 + 5i) / (2 - 5i)(2 + 5i) = (6 + 15i + 4i + 10i^2) / (4 + 25i^2) = (6 + 19i - 10) / (4 + 25(-1)) = -4 + 19i / 29 = (-4/29) + (19/29)i.

4. What is the complex conjugate of a complex number?

The complex conjugate of a complex number is the number with the same real component, but the imaginary component is the opposite sign. For example, the complex conjugate of 3 + 4i is 3 - 4i. This is useful when dividing complex numbers, as it eliminates the imaginary component from the denominator.

5. How are complex numbers represented on a graph?

Complex numbers can be represented on a graph using the complex plane, also known as the Argand diagram. The real component is represented on the horizontal axis, and the imaginary component is represented on the vertical axis. The point (a,b) in the complex plane represents the complex number a + bi. The distance from the origin to the point is known as the modulus, and the angle between the positive real axis and the line connecting the origin and the point is known as the argument or phase angle of the complex number.

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