12th Mathematics Ch 2

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1. i^n + i^n+1 + i^n+2 + i^n+3

1 point

(1) 0

(2) 1

(3) -1

(4) i

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2. The value of Summation i= 1 to 13 (i^n + i^n-1)is

1 point

(1) 1+i

(2) i

(3) 1

(4) 0

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3. The area of the triangle formed by the complex numbers z, iz, and z+iz in the Argand's diagram is

1 point

(1) 1/2 |z|^2

(2) |z|^2

(3) 3/2 |z|^2

(4) 2 |z|^2

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4. The conjugate of a complex number is 1/ (i-2). Then, the complex number is

1 point

(1) 1/ (i +2)

(2) -1/ (i+2)

(3) -1/ (i -2)

(4) 1/ (i -2)

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5. if z = [(√3+i)^3 (3i+4)^2] ÷ [8+6i]^2, then |z| is equal to

1 point

(1) 0

(2) 1

(3) 2

(4) 3

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6. If z is a non zero complex number, such that 2iz^2 = z^— then |z | is

1 point

(1) 1/2

(2) 1

(3) 2

(4) 3

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7. If |z-2+i| ≤ 2, then the greatest value of. |z| is

1 point

(1) √3-2

(2) √3+2

(3) √5-2

(4) √5+2

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8. If |z-3/2|=2, then the least value of |z| is

1 point

(1) 1

(2) 2

(3) 3

(4) 5

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9. If |z|=1, then the value of (1+z) ÷ (1-z) is

1 point

(1) z

(2) z^—

(3) 1/z

(4) 1

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10. The solution of the equation |z| - z =1+2i is

1 point

(1) 3/2 - 2i

(2) -3/2 + 2i

(3) 2-3/2i

(4) 2+3/2i

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11. If |Z1|=1, |Z2I=2, |z3|= 3 and |9Z1Z2+4Z1Z3+Z2Z3|=12, then the value of |Z1+Z2+Z3| is

1 point

(1) 1

(2) 2

(3) 3

(4) 4

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12. If z is a complex number such that ZE C/R and Z+1/Z eR, then is

1 point

(1) 0

(2) 1

(3) 2

(4) 3

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13. Z1, Z2 and Z3 are complex numbers such that Z1+Z2+Z3=0 |Z1|=|Z2|=|Z3|=1 then Z1^2 + Z2^2 +Z3^2 is

1 point

(1) 3

(2) 2

(3) 1

(4) 0

Clear selection

14. If (z-1) / (z+1) is purely imaginary, then |z| is

1 point

(1) 1/2

(2) 1

(3) 2

(4) 3

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15. If z=x+iy is a complex number such that |z+2| = |z-2|, then the locus of z is

1 point

(1) real axis

(2) imaginary axis

(3) ellipse

(4) circle

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16. The principal argument of 3/(-1+i)Is

1 point

(1) -5π/6

(2) -2π/3

(3) -3π/4

(4) -π/2

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17. The principal argument of (sin 40° +icos 40°)^5 is

1 point

(1)-110°

(2) -70°

(3) 70°

(4) 110°

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18. IF (1+i)(1+2i)(1+3i)--(1+ni)=x+iy, then 2.5.10...(I+n^2) is

1 point

(1) 1

(2) i

(3) x^2 +y^2

(4) 1+n^2

Clear selection

19. If w ≠1 is a cubic root of unity and (I+w)7 = A+Bw, then (A,B) equals

1 point

(1) (1,0)

(2) (-1,1)

(3) (0,1)

(4) (1,1)

Clear selection

20. The principal argument of the complex number (1+i√3)²/4i(1-i√3) is

1 point

(1) 2π/3

(2) π/6

(3) 5π/6

(4) π/2

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21. If a and B are the roots of x²+x+1=0, then a^2020+b^2020 is

1 point

(I) -2

(2) -1

(3) 1

(4) 2

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22. The product of all four values of (cosπ/3 +isin π/3)¾ is

1 point

(1) -2

(2) -1

(3) 1

(4) 2

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23. If w≠1 is a cubic root of unity and image then k is equal to

1 point

(1) 1

(2) -1

(3) √3i

(4) -√3i

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24. The value of [(1+√3i)/(1-√3i)]^10 is

1 point

(1) cis 2π/3

(2) cis 4π/3

(3) -cis 2π/3

(4) -cis 4π/3

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25.

1 point

(1) 1

(2) 2

(3) 3

(4) 4

Clear selection

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