1a.)Write i + 3 in the form R e^(i). Write as a rational number times . b) Do the same for i 3. c)Show that the two square roots of R e^(i) are R e^(i/2) . Hint: This is easy! Don't work too hard. d. Use the result of c. to find the square roots of 2i and 2 + 2i 3.

2. Find all six solutions to the equation z^6 = 1 and write each in the form A + iB and plot them in the complex plane. Hint: write z = Re^(i) for R real and positive, and find R and

3.

1.5. Find three independent solutions to the differential equation (5\" @f(t_l+f(i)=0- |You should use complex exponentisls to derive the solutions, but express the results in real Iform