Consider two complex numbers, x and y satisfying |x|=|y| and Arg(x)+Arg(y)=π. What is x in terms of y?
Consider two complex numbers, x and y satisfying |x|=|y| and Arg(x)+Arg(y)=π. What is x in terms of y? Correct Answer -y̅
Let |x|=|y|=r, therefore, x=reiα and y=reiβ, where, α+β=π, Hence, x=rei(π-β)=reiπe-iβ Therefore, x=-re-iβ=-y̅.
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Feb 20, 2025
