COMPLEX ANALYSIS QUESTIONS
1.Evaluate the integral ∫C(z2−2⋅z−3)dz
Where C
Is the curve given by x(t)=−3⋅t
And y(t)=−2⋅t
With −1≤t≤1
First you want to express your integral in the form
∫1−1f(z(t))z′(t)dt
Using the parameterization of the curve. Here
F(z(t))=
And
Z′(t)=
Now
∫1−1f(z(t))z′(t)dt=
2.a) Write the complex number8 z=(4i+8)/(4i+5) in the form8a+bi
8z =
b.)Given the complex numbers z = 14−12⋅i
and w = 8−3⋅i, evaluate and write in the form a+bi, where a And b Are real
numbers
Z¯+w¯=
Z+w¯¯¯¯¯¯¯¯¯¯¯¯=
Z¯−w¯¯¯¯¯¯¯¯¯¯¯¯¯¯=
Z−w¯¯¯¯¯¯¯¯¯¯¯¯=
Z×z¯=
3.Consider the complex number z=(5/2)+(5⋅3√⋅i)/2
Use De Moivre’s Theorem to find z^3
