## Amplitude (Argument) of Complex Numbers MCQ Advance Level

Compared to other sections, mathematics is considered to be the most scoring section. If prepared thoroughly, mathematics can help students to secure a meritorious position in the exam. These questions are very important in achieving your success in Exams after 12th.

Q1. If complex number z=x+iy is taken such that the amplitude of fraction (z-1)/(z+1) is always Ï€/4, then

•  x2 + y2 + 2y = 1
•  x2 + y2 - 2y = 0
•  x2 + y2 + 2y = - 1
•  x2 + y2 - 2y = 1

x2 + y2 - 2y = 1

Q2. If z1=10+6i, z2=4+6i and z is a complex number such that amp ((z-z1)/(z-z2))=Ï€/4 then the value of | z – 7 – 9i | is equal to

•  √2
•  2 √2
•  3 √2
•  2 √3

3 √2

Q3. If z1 = 8 + 4 i, z2 = 6 + 4 i and arg ((z-z1)/(z-z2))=Ï€/4, then z satisfies

•  | z – 7– 4i | = 1
•  | z – 7– 5i | = √2
•  | z – 4i | = 8
•  | z – 7i | = √18

| z – 7– 5i | = √2

Q4. If z1, z2 and z3, z4 are two pairs of conjugate complex numbers, then arg(z1/z4)+arg(z2/z3) equals

•  0
•  Ï€/2
•  3Ï€/2
•  Ï€

0

Q5. If z1=a+ib and z2=c+id are complex numbers such that |z1|=|z2|=1 and R(z conj(z))=0, then the pair of complex numbers w1=a+ic and w2=b+id satisfies

•  | w1 | = 1
•  | w2 | = 1
•  R(w1 conj(w2))=0
•  All the above

All the above

Q6. If amp (Z-2)/(2z+3i)=0 and z0=3+4i then

•  z0 conj(z) + conj(z0) z = 12
•  z0 z + conj( z0) conj(z) = 12
•  z0 conj(z) + conj(z0) z = 0
•  None of these

z0 z + conj( z0) conj(z) = 12

Q7. If amp (z1 z2)=0 and |z1|=|z2|=1 then

•  z1 + z2 = 0
•  z1 z2 = 1
•  z1=conj(z2)
•  both (b) and (c)

both (b) and (c)

Q8. If |z1+z2|2 = |z1|2 + |z2|2 then

•  z1/z2 is purely imaginary
•  z1 conj(z2) + z2 conj(z1)= 0
•  amp z1/z2 = Ï€/2
•  All of these

All of these

Q9. Let z1=[(√3 + i)2.(1-√3 i)]/(1 + i), z2=[(1 + √3 i)2.(√3 - i)]/(1 - i). Then

•  | z1| = | z2|
•  amp z1 + amp z2 = 0
•  3| z1| = | z2|
•  3 amp z1 + amp z2 = 0

3 amp z1 + amp z2 = 0

Q10. If z1 and z2 both satify z + conj(z)=2 | z - 1 | and arg(z1-z2)= Ï€/4, then the imaginary part of (z1+z2) is

•  0
•  1
•  2
•  None of these

2

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