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Greg
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Prove that $\arg[(a+bi)(c+di)]=\arg(a+bi)+\arg(c+di)$.
greg1313 said:Prove that $\arg[(a+bi)(c+di)]=\arg(a+bi)+\arg(c+di)$.
greg1313 said:Prove that $\arg[(a+bi)(c+di)]=\arg(a+bi)+\arg(c+di)$.
ZaidAlyafey said:I suppose you mean the principle argument because the given function is multivalued!
On the contrary, the result is false if you insist on the principal value of the argument, because the left and right sides can differ by $2\pi.$ZaidAlyafey said:I suppose you mean the principle argument because the given function is multivalued!
Opalg said:On the contrary, the result is false if you insist on the principal value of the argument, because the left and right sides can differ by $2\pi.$
Opalg said:On the contrary, the result is false if you insist on the principal value of the argument, because the left and right sides can differ by $2\pi.$
greg1313 said:I should have put more thought into what I was asking. My apologies and thanks for the replies.
A "Complex Number Challenge" is a mathematical problem or puzzle that involves complex numbers. Complex numbers are numbers that have both a real and imaginary component, and are often represented as a + bi, where a is the real part and bi is the imaginary part.
Complex numbers are important in science because they allow us to represent and solve problems that cannot be solved with real numbers alone. They are used in many fields such as physics, engineering, and economics to model and understand complex systems and phenomena.
Some examples of "Complex Number Challenges" in science include solving differential equations, finding the roots of polynomial equations, and modeling electrical circuits. These challenges often require the use of complex numbers to find solutions.
Scientists use complex numbers in their research in a variety of ways. For example, in physics, complex numbers are used to describe the behavior of quantum systems. In engineering, they are used to analyze and design electronic circuits. In economics, they are used to model financial markets and predict trends.
Some strategies for solving "Complex Number Challenges" include converting the problem to polar form, using the properties of complex numbers, and graphing the problem on the complex plane. It is also important to understand the basics of complex arithmetic and how to manipulate complex numbers to simplify the problem.