## Representation of Complex Numbers MCQ Basic 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 x + 1/x = √3, then x =

•  cos Ï€/3 + i sin Ï€/3
•  cos Ï€/2 + i sin Ï€/2
•  sin Ï€/6 + i cos Ï€/6
•  cos Ï€/6 + i sin Ï€/6

cos Ï€/6 + i sin Ï€/6

Q2. √3 + i =

•  cos Ï€/6 + i sin Ï€/6
•  2(cos Ï€/6 + i sin Ï€/6 )
•  2(cos Ï€/3 + i sin Ï€/3 )
•  None of these

2(cos Ï€/6 + i sin Ï€/6 )

Q3. If (1 + i√3)9 = a + ib, then b is equal to

•  1
•  256
•  0
•  93

0

Q4. If x = cos Î¸ + i sin Î¸ and y = cos Ï† + i sin Ï†, then xmyn + x- my- n is equal to

•  cos( m Î¸ + n Ï†)
•  cos( m Î¸ - n Ï†)
•  2 cos( m Î¸ + n Ï†)
•  2 cos( m Î¸ - n Ï†)

2 cos( m Î¸ + n Ï†)

Q5. If z = rei Î¸, then | eiz | =

•  er sin Î¸
•  e- r sin Î¸
•  e- r cos Î¸
•  er cos Î¸

e- r sin Î¸

Q6. If z = (√3/2 + i/2)5 + (√3/2 - i/2)5, then

•  Re (z) = 0
•  Im (z) = 0
•  Re (z) > 0, Im (z) > 0
•  Re (z) > 0, Im (z) < 0

Im (z) = 0

Q7. ((1 + cos Ï† + i sin Ï†)/ (1 + cos Ï† + i sin Ï†))n

•  cosn Ï† - i sinn Ï†
•  cosn Ï† + i sinn Ï†
•  sinn Ï† + i cosn Ï†
•  sinn Ï† - i cosn Ï†

cosn Ï† + i sinn Ï†

Q8. If n is a positive integer, then (1+i)n + (1-i)n is equal to

•  (√2)n-2 cos(nÏ€/4)
•  (√2)n-2 sin(nÏ€/4)
•  (√2)n+2 cos(nÏ€/4)
•  (√2)n+2 sin(nÏ€/4)

(√2)n+2cos(nÏ€/4)

Q9. If y = cos Î¸ + i sin &thetha;, then the value of y + 1/y is

•  2 cos Î¸
•  2 sin Î¸
•  2 cosec Î¸
•  2 tan Î¸

2 cos Î¸

Q10. The polar form of the complex number (i25)3 is

•  cos Ï€/2 + i sin Ï€/2
•  cos Ï€ + i sin Ï€
•  cos Ï€ - i sin Ï€
•  cos Ï€/2 - i sin Ï€/2

cos Ï€/2 - i sin Ï€/2

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