If - z -3 i - - 5 then the minimum value of - z -2- will beA- 0B- 2 - 5-13D- 1

The correct option is A 0|z 3i| ≤ 5 ⇒ (x)^2 + (y nbsp; 3)^2 ≤ 25 Putting y = 0, x^2 nbsp; + 9 = 25 ⇒ x = ± 4 The minimum of |z + 2| will occur at z ...

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Standard XII

Mathematics

Inequality of 2 Complex Numbers

If | z -3 i |...

Question

If $| z - 3 i | \leq 5$ then the minimum value of $| z + 2 |$ will be

0

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Solution

The correct option is A $0$
$| z - 3 i | \leq 5 \Rightarrow (x)^{2} + (y - 3)^{2} \leq 25$
Putting $y = 0$ ,
$x^{2} + 9 = 25 \Rightarrow x = \pm 4$

The minimum of $| z + 2 |$ will occur at $z = - 2$ and the minimum value is $0$

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If |z−3i|≤5 then the minimum value of |z+2| will be

The correct option is A 0|z−3i|≤5⇒(x)2+(y−3)2≤25 Putting y=0, x2+9=25⇒x=±4 The minimum of |z+2| will occur at z=−2 and the minimum value is 0

If $| z - 3 i | \leq 5$ then the minimum value of $| z + 2 |$ will be

The correct option is A $0$
$| z - 3 i | \leq 5 \Rightarrow (x)^{2} + (y - 3)^{2} \leq 25$
Putting $y = 0$ ,
$x^{2} + 9 = 25 \Rightarrow x = \pm 4$

The minimum of $| z + 2 |$ will occur at $z = - 2$ and the minimum value is $0$