1) Let z =-1 =3j be a complex number. Sketch the number in thecomplex plan. Find the magnitude (absolute value) and argument(angle) of z (be careful of the quadrant in the complex plane ).Write z in Euler's form z =|z|eapjφ.
2) Let z =6exp j(π/3). Sketch the number in the complexplane . Find Re (z) (real part of z ) and Im (z) (imagainary partof z). Find the complex conjugate of z.
3) Generate an analogous diagram for a closed-loop controlsystem to maintain the water level in a tank that has a singleinlet valve (that can be controlled )and an unknown leak. Anexample of a closed -loop system such as this is the tank on atoilet. Identify all of the blocks of the closed -loop system andthe various sigaals in the loop such as the "Reference,"the"output," and the "Disturbances.' In a sentence or two,explain thelogic the controller might use.Explain the advantages and disadvantages of the control system described above compared to anopen-loop version of the system. Be specific to this example.