If -z-3 i-3- where i-1 and z -0- -2- then z-6-z is equal to

The correct option is D i put z cosθ + i sinθ, we get |cosθ + i sinθ 3i| = 3 ⇒ sinθ = 1/6 ∴ cotθ 6/z = i ...

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Solving Simultaneous Trigonometric Equations

If |z-3 i|=3,...

Question

If |z - 3i| = 3, (where i = $\sqrt{- 1}$ ) and argz $\in (0, \frac{π}{2})$ , then cot(arg(z)) - $\frac{6}{z}$ is equal to

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| z - 3 i | = 3

a r g z \in (0, \frac{π}{2})

c o t (a r g z) - \frac{6}{z}

z

θ, 0 < θ < π / 2

| z - 3 i | = 3

cot θ - \frac{6}{z}

z = \sqrt{3 + 4 i} + \sqrt{- 3 + 4 i}

\pm \frac{π}{4}, \pm \frac{3 π}{4}

\sqrt{- 1} = i

\sqrt{z} = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \sqrt{\frac{| z | + R e (z)}{2}} + i \sqrt{\frac{| z | - R e (z)}{2}} & , if B > 0 \sqrt{\frac{| z | + R e (z)}{2} - i \sqrt{\frac{| z | - R e (z)}{2}}} & , if B < 0 \end{matrix}

z + \sqrt{2} | z + 1 | + i = 0,

i = \sqrt{- 1}

| z |

If $| z - i | = 1$ and arg $(z) = θ$ where $θ \in (0, \frac{π}{2})$ , then
$c o t θ - \frac{2}{z}$

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