1. [1pt] Which of the formulae is false? (could be more than one)
(A) z1z2=z1z2
(B) arg z= arg z
(C) |z|=|z|
(D) z1+z2=z1+z2
(E) z1z2=z1z2for z26= 0.
2. [1pt] Which of the formulae is false? (could be more than one)
(A) |z1z2|=|z1||z2|
(B) arg(z1z2) = arg z1+ arg z2
(C) |z1+z2| ≤ |z1|+|z2|
(D) arg(z1+z2) = arg z1+ arg z2
(E) for z26= 0, arg z1
z2= arg z1−arg z2.
3. [1pt] Which of the formulae is false?(could be more than one)
(A) eu+iv = eu(cos v+isin v)
(B) ln(2i) = ln 2 + i(π
2+ 2πk), k ∈Z.
(C) eiπ =−1
(D) e|z|=|ez|(E) ez= 1 + z+z2
2+z3
3! +. . .
4. [1pt] The set of solutions of the equation
e2z+ ez+1 + ez+ e = 0 is
(A) z= (k+ 1)πi, 1 + (2k+ 1)πi, k ∈Z
(B) z= (k−1)πi, 1 + (4k+ 1)πi, k ∈Z
(C) z= (2k+ 1)πi, 1 + (2k+ 1)πi, k ∈Z
(D) z= (2k+ 1)πi, k ∈Z
(E) z= 1 + (2k+ 1)πi, k ∈Z
5. For the following numbers z(in order)
1 + iπ
2,1−3 i π
4,1−iπ
6,1−iπ
3
choose the correct order of ez
(A)
i e,√2
2e−i√2
2e,√3
2e−ie
2,e
2−i√3
2e
(B) √3
2e−ie
2,i e,√2
2e−i√2
2e,e
2−i√3
2e
(C) √2
2e−i√2
2e,i e,√3
2e−ie
2,e
2−i√3
2e
(D) √2
2e−i√2
2e,√3
2e−ie
2,i e,e
2−i√3
2e
(E) none of these orders of answers is correct.
1
Complex Analysis
