Complex number need an idea to start

Thread starter naspek
Start date Nov 29, 2009
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Complex Complex number Idea

In summary, complex numbers are numbers that contain both a real part and an imaginary part, represented by the letter "i." They are used to solve equations that cannot be solved with just real numbers and to represent physical quantities. To add or subtract complex numbers, you combine the real and imaginary parts separately. Multiplication and division can be done using the FOIL method and the conjugate of the denominator. The polar form of a complex number is a way to represent it in terms of magnitude and angle, useful for calculations. In real life, complex numbers are used in various fields such as science, engineering, computer graphics, and finance to understand and model complex systems and phenomena.

Nov 29, 2009

naspek

Homework Statement

Find the principal value of i^2i

Homework Equations

principal value = Ln r + iArg(z)

The Attempt at a Solution

dont know how to start..

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Nov 29, 2009

jgens

Gold Member

Hint: [itex]i^{2i} = e^{2i\ln{i}}[/itex]

Related to Complex number need an idea to start

What are complex numbers and why do we need them?

Complex numbers are numbers that contain both a real part and an imaginary part. The imaginary part is represented by the letter "i," which stands for the square root of -1. We need complex numbers to solve equations that cannot be solved with just real numbers, and to represent physical quantities like electrical current and voltage.

How do you add and subtract complex numbers?

To add or subtract complex numbers, you simply combine the real parts and the imaginary parts separately. For example, (2 + 3i) + (4 - 2i) = (2 + 4) + (3i - 2i) = 6 + i. For subtraction, you just change the sign of the second complex number and follow the same process.

Can you multiply and divide complex numbers?

Yes, you can multiply and divide complex numbers using the FOIL method (First, Outer, Inner, Last). For example, (2 + 3i)*(4 - 2i) = (2*4) + (2*-2i) + (3i*4) + (3i*-2i) = 8 + (-4i) + (12i) + (-6i^2) = 8 + 8i - 6(-1) = 8 + 8i + 6 = 14 + 8i. Division is done by multiplying the numerator and denominator by the conjugate of the denominator, which is the same expression but with the opposite sign for the imaginary part.

What is the polar form of a complex number?

The polar form of a complex number is a way to represent it in terms of its magnitude (or distance from the origin) and its angle. It is written as r(cosθ + isinθ), where r is the magnitude and θ is the angle (in radians). This form is useful for performing calculations and simplifying complex numbers.

How are complex numbers used in real life?

Complex numbers are used in many fields of science and engineering, including electromagnetics, quantum mechanics, signal processing, and fluid dynamics. They are also used in computer graphics and animations, as well as in finance and economics. Complex numbers help us understand and model complex systems and phenomena in the physical world.