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For the complex number z = 1 - t + i√(t² + t + 2), where t is a real parameter, the path traced by z in the Argand plane is

1. an ellipse
2. a hyperbola
3. a straight line
4. none of these

Correct answer: a hyperbola

Solution

The expression for the complex number z can be separated into its real and imaginary parts, where the real part is linear in t and the imaginary part is quadratic in t. This combination of a linear term and a quadratic term in the complex plane typically represents a hyperbolic path.

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