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Macarenses
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How does one prove that for w≠+-1 , w a complex number, there are exactly 2 solutions to the equation w=0.5(z+1/z)? I'm at a total loss here. Could someone clue me in on this one?
What if you multiplied each side by 2z?Macarenses said:How does one prove that for w≠+-1 , w a complex number, there are exactly 2 solutions to the equation w=0.5(z+1/z)? I'm at a total loss here. Could someone clue me in on this one?
I do believe that the quadratic formula will work for equations with complex coefficients even if it is not clear (at least to me) how to find the square root of a complex number. Just write the solution out in the radical form simplified as far as posible.HallsofIvy said:The best way to prove there are two solutions is to find them! That is what ramsey2879 is suggesting.
The process for solving for w in a complex equation involves manipulating the equation using algebraic operations to isolate the variable w on one side of the equation. This may include combining like terms, using the distributive property, and applying inverse operations.
To check if your solution for w is correct, you can substitute the value of w back into the original equation and see if it satisfies the equation. If it does, then your solution is correct. You can also check your work by using a graphing calculator or solving the equation using a different method.
Some common mistakes to avoid when solving for w in a complex equation include forgetting to distribute a negative sign, making a calculation error, or incorrectly applying the order of operations. It is important to double check your work and identify any potential errors.
Yes, you can use the quadratic formula to solve for w in a complex equation, as long as the equation is in the form of ax^2 + bx + c = 0. However, in some cases, the solutions for w may be complex numbers instead of real numbers.
There are no specific shortcuts or tricks for solving complex equations for w, but it can be helpful to simplify the equation as much as possible before attempting to solve for w. Breaking down the problem into smaller, more manageable steps can also make the process easier.