Answer to Question #218562 in Complex Analysis for Unknown346307

Complex Analysis

Question #218562

If z is a complex number and |z + 16| = 4 |z + l|, find the value of | z|

Expert's answer

z=x+yi

|z+16|=4|z+1|

|x+yi+16|²=4²|x+yi+1|²

[(x+16)²+y²]=16[(x+1)²+y²]

x²+32x+256+y²=16x²+32x+16+16y²

15x²+15y²=240

x²+y²=16

|z|=|x+yi|=4

Learn more about our help with Assignments: Complex Analysis

Comments

No comments. Be the first!

Leave a comment

Related Questions

1. if f(z) is an analytical function of z, then prove that ( d^2/dx^2 + d^2/ dy^2) log |f(z)|= 0
2. Expand f(z)=𝑧+3/𝑧(𝑧2−𝑧−2) in power of z wherea) |𝑧|<1b) 1<|𝑧|<2c) |�
3. Find the Taylor's theorem expansion of logz=(z-1) -(z-1) ²/2+(z-1) ³/2-........., when |z-1|&
4. Find the value of ∫c 1/𝑍𝑑𝑧, where C is circle 𝑧=𝑒^𝑖∅, 0≤∅≤𝜋
5. Expand f(z)=𝑧+3/𝑧(𝑧2−𝑧−2) in power of z wherea) |𝑧|<1b) 1<|𝑧|<2c) |�
6. Find the smallest value of P=|z-2|^2 + |z+1-i|^2 + | z-2 -5i| And z (z = x +yi : x,y are real numbe
7. Expand f(z)= "Expand f(z)= \ud835\udc67+3\ud835\udc67(\ud835\udc672\u2212\ud835\udc67\u22122)\nin po