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Vector Equation for Straight Line

39. Point z m...

Question

39. Point z moves on curve |z-3i-4|+|z-5-12i|=82 value of |z|min+|z|max is 1) 10 2)18

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Solution

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| z - 4 - 3 i | = 2

| z - 5 i | + | z - 11 i | = 10

| z |

3

| z |

\frac{\sqrt{39}}{4}

tan (min arg z)

13

tan (max arg z)

10 + \frac{\sqrt{39}}{4}

^{'} z^{'}

| z - 4 - 3 i | = 2

| z |

a r g (z + i) = \frac{π}{4}

| z + 4 - 3 i | + | z - 4 + 3 i |

P (z)

z ¯ ¯ ¯ z + (4 - 5 i) ¯ ¯ ¯ z + (4 + 5 i) z = 40.

a = max | z + 2 - 3 i |

b = min | z + 2 - 3 i |,

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