A complex modulus in the Argand diagram has a tangent which cuts real–axis at `2` with slope `-2/3`, and the modulus cuts the imaginary axis at `bi` and `ci` as well, where `b` and `c` are the roots of the equation `x^2 – 6x + k = 0`, where `k` is a constant. Find `b`, `c` and `k`.

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