The complex number satisfying z - i -4 and 2 z -3-2 i -3 -4 simultaneously isA- 3-4-1-4 iB- -1-4-3-4 iC- None D- 1-4-3-4 i

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The complex number satisfying arg (z + i) = $\frac{π}{4}$ and arg (2z + 3 - 2i) = $\frac{3 π}{4}$ simultaneously is

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arg (z - 3 i) = \frac{3 π}{4}

arg (2 z + 1 - 2 i) = \frac{π}{4}

arg [\frac{(z - 5 + 4 i)}{(z + 3 - 2 i)}] = - \frac{π}{4}

arg (\frac{(z - 5 + 4 i)}{(z + 3 - 2 i)}) = - \frac{π}{4}

z

arg (\frac{3 z - 6 - 3 i}{2 z - 8 - 6 i}) = \frac{π}{4}

| z - 3 + 4 i | = 3.

z

arg [z - (1 + i)] = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ \begin{matrix} \frac{3 π}{4} & ; | z | \leq | z - 2 | - \frac{π}{4} & ; | z | > | z - 2 | \end{matrix}

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