10(cos(4pi/3) + i sin(4pi/3))
To multiply complex numbers in trigonometric form, you simply multiply the radii and add the thetas. We have:
z1=5(cos(pi/2)+i sin(pi/2))
z2=2(cos(5pi/6)+i sin(5pi/6))
The radii for the above 2 numbers are 5 and 2. So the result will have a radius of 5*2 = 10. The thetas are pi/2 and 5pi/6, so the new theta will be pi/2 + 5pi/6 = 3pi/6 + 5pi/6 = 8pi/6 = 4pi/3. So the answer is:
10(cos(4pi/3) + i sin(4pi/3))
