For the real parameter t, the locus of the co | vedclass

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(B) Given the complex number $z = (1 - t^2) + i \sqrt{1 + t^2}$.Let $z = x + iy$, where $x$ and $y$ are real numbers.Equating the real and imaginary p

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a parabola

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(B) Given the complex number $z = (1 - t^2) + i \sqrt{1 + t^2}$.Let $z = x + iy$, where $x$ and $y$ are real numbers.Equating the real and imaginary parts, we get:$x = 1 - t^2$$y = \sqrt{1 + t^2}$Squaring the imaginary part, we have $y^2 = 1 + t^2$.From the first equation, $t^2 = 1 - x$.Substituting this into the equation for $y^2$:$y^2 = 1 + (1 - x)$$y^2 = 2 - x$$y^2 = -(x - 2)$This is the standard equation of a parabola of the form $Y^2 = -4aX$ with vertex at $(2, 0)$.

For the real parameter $t$, the locus of the complex number $z = (1 - t^2) + i \sqrt{1 + t^2}$ in the complex plane is

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