todai-math 2021 QII

todai-math · Japan · todai-engineering-math__paper3 Complex Numbers Argand & Loci Locus Identification from Modulus/Argument Equation
Deduce the conditions for $z$ and, on the complex $z$ plane, draw the area of $z$ in which the imaginary part of the complex function $J(z) = e^{-i\alpha} z + e^{i\alpha} z^{-1}$ is positive. Here, $\alpha$ is a real number and $0 < \alpha < \pi/2$.
Deduce the conditions for $z$ and, on the complex $z$ plane, draw the area of $z$ in which the imaginary part of the complex function $J(z) = e^{-i\alpha} z + e^{i\alpha} z^{-1}$ is positive. Here, $\alpha$ is a real number and $0 < \alpha < \pi/2$.
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