3598：A secret of 《The Tai Chi Master》

Do you remember a TV play called “The Tai Chi Master” in 1990s. In this play, the leading role Yang Yuqian (actor is Wu Jing) is fond of Tai Ji and becomes a great master at last. However, the Chen Style Taiji was only open to family Chen. So Yang Yuqian decides to steal the skill with the help from a teenager called Chen Shaoqi. They are best friends, and Shaoqi is the “son” of Chen family leader. But one day, Chen Zhenying, Shaoqi’s father, found Yang Yuqian and decided to drive him away. Chen Zhenying is interested in math. So he gives Yang Yuqian a chance: if Yang can solve his problem, then Yang can be his new apprentice.


The problem is that : C is a circle of Taiji in figure-1. In figure-2, the C is a circle and its centre is (0, 0). Its radius is R.is a line integral in plural plane according to the circle C and its direction is anti-clockwise. We define The Yang Yuqian’s dream will come true only if  I  is calculated.

Multiply cases. First line is number of test cases.
Each test case consisted of 7 integers. a,b,c,d,x,y,R represent the a,b,c,d,R in description and x,y represent the real part and imaginary part of Z₀. a,b,c,x,y∈(-10000,10000);d∈(-10000,0)∪(0,10000);R∈(0,10000)

Each test case is printed one line. If the answer is plural, the output format is a±bi . If the answer is real number, output it as writing habits. All real numbers are round to 4 decimals.