Complex Analysis Answers

Find number of roots of equation z^2-ae^z=0, where 0<a<e^-1, and |z|<1

Find residue of function f(z)=exp(1/z^2)*cos(z) at point z=0

show that the equation |Z-Zo| =R of the circle centered at Zo with radius R can be written as
|Z| square -2Re(ZZo bar) + |Zo|square = R square

2. From the data given below calculate the value of first and third quartiles, second and ninth deciles and forty-fifth and fifty-seventh percentiles.

Height in
centimeters Number of
students Cumulative
frequency
161-167 79 79
167-173 92 171
173-179 60 231
179-185 22 253
185-191 5 258
191-197 2 260
Total 260

5. The ages of husbands and wives in a community were found to have a correlation coefficient equal to +0.8; the average of husbands’ ages was 25 years and that of wives’ ages 22 years; their standard deviations were respectively 4 and 5 years. Find the two lines of regression and from the lines ,measure
a. The expected age of husband when wife’s age is 12 years
b. The expected age of wife when husband’s age is 33 years