Locus of z when (z - a)/(z - b) is purely real or purely imaginary

1. A.
   $S$ contains exactly two elements
2. B.
   $S$ contains only one element
3. C.
   $S$ is a circle in the complex plane
4. D.
   $S$ is a straight line in the complex plane

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1. A.
   $2\sqrt{2} - 1$
2. B.
   $3\sqrt{2}$
3. C.
   $6\sqrt{2}$
4. D.
   $2\sqrt{2}$

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1. A.
   $\frac{3}{2}$
2. B.
   $\frac{4}{3}$
3. C.
   $\frac{2}{3}$
4. D.
   $\frac{3}{4}$

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1. A.
   $y + x^{2} + y^{2} \neq - \frac{1}{4}$
2. B.
   $x = 0$
3. C.
   $(x,y) = \left( 0, - \frac{1}{2} \right)$
4. D.
   $y \in \left( - \infty, - \frac{1}{2} \right) \cup \left( - \frac{1}{2},\infty \right)$

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1. A.
   12
2. B.
   $\infty$
3. C.
   10
4. D.
   8

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1. A.
   both are incorrect
2. B.
   only (S1) is correct
3. C.
   only (S2) is correct
4. D.
   both are correct

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