Show the following hold for complex numbers z, w C: (a) Re(2) Re(z)| |z]....

 

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Show the following hold for complex numbers z, w € C: (a) Re(2) ≤ Re(z)| ≤|z]. (b) Im(2) ≤| Im(2)| ≤ |z|. (c) |zw| = |z||w|. (d) |z| = |2| (e) | Re(2)| + |Im(2)| ≤ √2|2|. (10 presentation points) Problem 2 Characterize cases of equality in the inequalities (a), (b) and (e) in Problem 1 above. (10 presentation points) Show the following hold for complex numbers z, w € C: (a) Re(2) ≤ Re(z)| ≤|z]. (b) Im(2) ≤| Im(2)| ≤ |z|. (c) |zw| = |z||w|. (d) |z| = |2| (e) | Re(2)| + |Im(2)| ≤ √2|2|. (10 presentation points) Problem 2 Characterize cases of equality in the inequalities (a), (b) and (e) in Problem 1 above. (10 presentation points)

Answer rating: 100% (QA)

a To show Re2 Re2 2 we can directly compute the values involved Re2 2 Re2 2 Therefore 2 2 2 Simplify... View the full answer