If -z-25 i- - 15- then -maxampz-minampz-

We have max amp(z) = amp(z_2), min amp (z) = amp(z_1) Now amp(z_1) = θ_1 = cos^ 1( 15/25) = cos^ 1( 3/5) amp(z_2) = π/2 + θ_2 = π/2 + sin^ 1( 15/25) = π/2 + ...

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Byju's Answer

If |z-25 i| ≤...

Question

If |z - 25i| $\leq$ 15, then |max amp(z) - min.amp(z)| =

c o s^{- 1} (\frac{3}{5})

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π - 2 c o s^{- 1} (\frac{3}{5})

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\frac{π}{2} + c o s^{- 1} (\frac{3}{5})

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s i n^{- 1} (\frac{3}{5}) - c o s^{- 1} (\frac{3}{5})

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Solution

The correct option is B $π - 2 c o s^{- 1} (\frac{3}{5})$
We have
$m a x a m p (z) = a m p (z_{2}), m i n a m p (z) = a m p (z_{1})$

Now $a m p (z_{1}) = θ_{1} = c o s^{- 1} (\frac{15}{25}) = c o s^{- 1} (\frac{3}{5})$
$a m p (z_{2}) = \frac{π}{2} + θ_{2} = \frac{π}{2} + s i n^{- 1} (\frac{15}{25}) = \frac{π}{2} + s i n^{- 1} (\frac{3}{5})$
$∴$ |max amp(z) - min amp(z)|
$= ∣ ∣ \frac{π}{2} + s i n^{- 1} \frac{3}{5} - c o s^{- 1} \frac{3}{5} ∣ ∣$
$= ∣ ∣ \frac{π}{2} + \frac{π}{2} c o s^{- 1} \frac{3}{5} - c o s^{- 1} \frac{3}{5} ∣ ∣ = π - 2 c o s^{- 1} \frac{3}{5}$

Suggest Corrections

If |z - 25i| ≤ 15, then |max amp(z) - min.amp(z)| =

If |z - 25i| $\leq$ 15, then |max amp(z) - min.amp(z)| =