if-z-6i-5-find-the-maximum-and-minimum-value-of-z-5-

Question Number 156520 by aliyn last updated on 12/Oct/21

i f ∣ z + 6 i ∣⩽ 5 f i n d t h e m a x i m u m a n d m i n i m u m v a l u e o f ∣ z + 5 ∣ ?

Answered by TheSupreme last updated on 12/Oct/21

x^{2} + {(6 + y)}^{2} ⩽ 5 (c i r c l e c e n t e r - 6 i r a d i u s \sqrt{5)}

{(x + 5)}^{2} + y^{2} = θ (x, y) (c i r c l e o f c e n t e r - 5 r a d i u s \sqrt{θ})

\sqrt{θ} + \sqrt{5} = \sqrt{5^{2} + 6^{2}}

\sqrt{θ} - \sqrt{5} = \sqrt{5^{2} + 6^{2}}

m i n = \sqrt{61} - \sqrt{5}

m a x = \sqrt{61} + \sqrt{5}