Keiner Nichts said:Homework Statement
If Z1+Z2+Z3=0 and Z1*Z2 + Z2*Z3 + Z3*Z1=0 and Z1, Z2, Z3 are all complex, what is the value of
(|z1|+|z2|+|z3|)/(|z1*z2|+|z2*z3|+|z3*z1|)
Homework Equations
The Attempt at a Solution
I tried to multiply the equations by the product of all conjugates and reach some equations but it lead to nothing in the end.[/B]
Complex numbers are numbers that contain both a real part and an imaginary part. They are typically written in the form a + bi, where a is the real part, b is the imaginary part, and i is the imaginary unit (equal to the square root of -1).
Complex numbers are used in a variety of scientific fields, including physics, engineering, and mathematics. They are particularly useful in solving problems involving electricity, magnetism, and waves.
A real number is a number that can be expressed on a number line, such as 3 or -2. A complex number, on the other hand, has both a real and imaginary component and cannot be represented on a number line.
To perform operations on complex numbers, you can use the rules of arithmetic for real numbers and also the fact that i^2 is equal to -1. For addition and subtraction, you simply combine the real parts and the imaginary parts separately. For multiplication, you use the FOIL method, and for division, you use the complex conjugate.
Complex numbers are particularly useful in solving problems that have no real solutions, such as equations involving the square root of a negative number. They also have applications in fields such as signal processing, quantum mechanics, and control systems.