What is the length of the darkened arc?
2 answers:
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Answer: complex equations has n number of solutions, been n the equation degree. In this case:
Step-by-step explanation:
I start with a variable substitution:
Then:
Solving the quadratic equation:
Replacing for the original variable:
or
Remembering that complex numbers can be written as:
Using this:
Solving for the modulus and the angle:
The possible angle respond to:
Been "RAng" the resultant angle, "Ang" the original angle, "n" the degree of the root and "i" a value between 1 and "n"
In this case n=4 with 2 different angles: Ang = 45º and Ang = 315º
Obtaining 8 different angles, therefore 8 different solutions.