Final answer:
The branch points of the multi-valued operation f(z) = [z² + (1-i)z - i]^1/4 can be found by setting the expression inside the square root to zero and solving for z. The branch points are the values of z that make the expression undefined. To sketch the branch points in the complex plane, plot the solutions to this equation.
Step-by-step explanation:
The branch points of the multi-valued operation f(z) = [z² + (1-i)z - i]^1/4 can be found by setting the expression inside the square root to zero and solving for z. The branch points are the values of z that make the expression undefined. In this case, the branch points are the solutions to the equation z² + (1-i)z - i = 0. To sketch the branch points in the complex plane, plot the solutions to this equation.