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Given z1 = 2∠45o


, ; z2 = 3∠120o and z3 = 4∠180o


. Determine the following and leave your


answers in rectangular form:


(i)


(z1)^2+z2/(z2 +z3)



(ii)


z1/z2z3





3. Use De Moivre’s Theorem to determine the cube root of Z and leave your answer in polar


form with the angle in radians


(a) Z = 1+i√3


3. Let Z = i

(i) Write Z in a polar form (2)

(ii) Use De Moivre’s Theorem to determine Z4


Let f(z)=1/z^5 . Use the polar form of the Cauchy Riemann equations to determine where f is differentiable

Let g(x, y) = y x2+y 2 . (a) Show that g is harmonic in D = {(x, y) : x 2 + (y + 3)2 < 4}. (b) How can the function f(z) = 1 z be used to show that g is harmonic in D? 


suppose f(z) =1/z. write f in the form f(z) = u(x,y) + iv(x,y), where z = x+iy and u and v are real-valued functions


Let A ={ z E C : Im (z+2/z-2)≥ 1}.

(a) Sketch the set A in the complex plane.

(b) Is z = −2i a boundary point of A? Provide reasons for your answer.

(c) Is this set open, closed, both or neither? Provide reasons for your answer.


Solve D2+4D+4=0 USING LAPLACE TRASFORMS


Let Z = i



(i) Write Z in a polar form



(ii) Use De Moivre’s Theorem to determine Z^4

Use De Moivre’s Theorem to determine the cube root of Z and leave your answer in polar


form with the angle in radians


(a) Z = 1+i√3


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