Complex Numbers: Unraveling the Mystery

Thread starter Hootenanny
Start date Oct 10, 2006
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Complex Complex numbers Numbers

In summary, complex numbers are numbers that have both a real and an imaginary part and are represented in the form a + bi. They are used to solve certain mathematical equations and are represented on a graph using the complex plane. The conjugate of a complex number is a reflection of the number over the x-axis, and operations on complex numbers involve adding, subtracting, multiplying, and dividing their real and imaginary parts.

Oct 10, 2006

Hootenanny

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[Deleted]. Figured it out

Last edited: Oct 10, 2006

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Oct 10, 2006

berkeman

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You big tease!

Oct 10, 2006

Hootenanny

Staff Emeritus

Science Advisor

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berkeman said:

You big tease!

:rofl: It was a stupid mistake, I felt embarrassed leaving it up there! :blushing:

Oct 10, 2006

3trQN

Complex indeed

1. What are complex numbers?

Complex numbers are numbers that have both a real and an imaginary part. They are written in the form a + bi, where a is the real part and bi is the imaginary part with i representing the square root of -1.

2. What is the purpose of using complex numbers?

Complex numbers are used to solve certain mathematical equations that cannot be solved with real numbers alone. They are also used in many fields of science and engineering, such as electrical engineering, quantum mechanics, and signal processing.

3. How are complex numbers represented on a graph?

Complex numbers are represented on a graph using the complex plane, where the real part is plotted on the x-axis and the imaginary part is plotted on the y-axis. The graph can be visualized as a 2-dimensional plane, with each point representing a different complex number.

4. What is the conjugate of a complex number?

The conjugate of a complex number a + bi is a - bi, where the sign of the imaginary part is changed. Geometrically, the conjugate of a complex number is a reflection of the number over the x-axis on the complex plane.

5. How do you perform operations on complex numbers?

To add or subtract complex numbers, you simply add or subtract the real and imaginary parts separately. To multiply complex numbers, you use the FOIL method (First, Outer, Inner, Last) and simplify the resulting terms. To divide complex numbers, you rationalize the denominator by multiplying by the conjugate of the denominator.