Presentation1_Radio.pptx
- 1. Analytic function
Mappings/ Transformation (translation, rotation and reflection)
Department of Physics
𝑧 = 𝑥 + 𝑖𝑦 𝑢, 𝑥, 𝑦 =? , 𝑣 𝑥, 𝑦 =?
Example: 𝑤 = 𝑓 𝑧 = 𝑧 + 1
𝑧2 = 𝑥 + 𝑖𝑦 ∗ 𝑥 + 𝑖𝑦 = 𝑥2 + 2𝑖𝑥𝑦 − 𝑦2 = 𝑥2 − 𝑦2 + 𝑖(2𝑥𝑦)
Hence, 𝑢, 𝑥, 𝑦 = 𝑥2
− 𝑦2
, 𝑣 𝑥, 𝑦 = 2𝑥𝑦
𝑧(3,1)
𝑤(8,6)
𝑢
𝑣