Trigonometric EquationHard
Question
If |z| = 1 and z ≠ ± 1, then all the values of 
lie on
lie on Options
A.a line not passing through the origin
B.|z| = √2
C.the x-axis
D.the y-axis
Solution
Let z = cosθ + sinθ, so that
Hence
lies on the imaginary axis i.e., x = 0.
Alternative
Let E =
which is imaginary.
Hence
lies on the imaginary axis i.e., x = 0. Alternative
Let E =
which is imaginary.
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