Question

$|z-25i|\le 15|max.amp\left(z\right)-min.amp\left(z\right)|=$

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

we have
$maxamp\left(z\right)=amp\left(z_2\right),minamp\left(z\right)=amp\left(z_1\right)$

$Nowamp\left(z_1\right)={\theta }_1=co{s}^{-1}\left(\frac{15}{25}\right)=co{s}^{-1}\left(\frac{3}{5}\right)$
$amp\left(z_2\right)=\frac{\pi }{2}+{\theta }_2=\frac{\pi }{2}+si{n}^{-1}\left(\frac{15}{25}\right)=\frac{\pi }{2}+si{n}^{-1}\left(\frac{3}{5}\right)$
$\therefore |maxamp\left(z\right)-minamp\left(z\right)-minamp\left(z\right)|=|\frac{\pi }{2}+si{n}^{-1}\frac{3}{5}-co{s}^{-1}\frac{3}{5}|$
$=|\frac{\pi }{2}+\frac{\pi }{2}-2co{s}^{-1}\frac{3}{5}|=\pi -2co{s}^{-1}\frac{3}{5}$