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$A$ value of $\theta$ for which $\frac{2 + 3i \sin \theta}{1 - 2i \sin \theta}$ is purely imaginary,is:

Which of the following statements is true?

If $(3x+2)-(5y-3)i$ and $(6x+3)+(2y-4)i$ are conjugates of each other,then the value of $\frac{x-y}{x+y}$ is (where $i=\sqrt{-1}, x, y \in R$ ).

$i^2 + i^4 + i^6 + \dots$ up to $(2n + 1)$ terms =

If $(1 - i)^n = 2^n$,then $n = $

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