## Real and imaginary parts of complex numbers, Algebraic operations, Equality of two 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 z(1+a)=b+ic and a2+b2+c2=1, then (1+iz)/(1-iz)=

•  √(a+ib)/1+c
•  -√(b-ic)/1+a
•  i√(a+ic)/1+b
•  None of these

√(a+ib)/1+c

Q2. Given that the equation z2+(p+iq)z+r+is=0 where, p, q, r, s are real and non-zero has a real root, then

•  pqr=r2+p2s
•  prs=q2+r2p
•  qrs=p2+s2q
•  pqs=s2+q2r

pqs=s2+q2r

Q3. If ∑ ik=x+iy(k=0 to 100), then the value of x and y are

•  x = –1, y = 0
•  x = 1, y = 1
•  x = 1, y = 0
•  x = 0, y = 1

x = 1, y = 0

Q4. Let (1-ix)/(1+ix)=a-ib and a2+b2=1, where a and b are real, then x=

•  2a/((1+a)2+b2)
•  2b/((1+a)2+b2)
•  2a/((1+b)2+a2)
•  2b/((1+b)2+a2)

2b/((1+a)2+b2)

Q5. If (1+i)(1+2i)(1+3i)....(1+ni)=a+ib, then 2 . 5 . 10.........(1+n2) is equal to

•  a2-b2
•  a2+b2
•  √(a2+b2)
•  √(a2-b2)

a2+b2

Q6. Given z=(q+ir)/(1+p), then (p+iq)/(1+r)=(1+iz)/(1-iz) if

•  p2+q2+r2=1
•  p2+q2+r2=2
•  p2+q2-r2=1
•  None of these

p2+q2+r2=1

Q7. If z1 and z2 are two complex numbers satisfying the equation |(z1+z2)/(z1-z2)|, then z1/z2 is a number which is

•  Positive real
•  Negative real
•  Zero or purely imaginary
•  None of these

Zero or purely imaginary

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Real and imaginary parts of complex numbers, Algebraic operations, Equality of two Complex numbers MCQ Advance Level