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1. The value of i^4, where i is the imaginary unit, is

A. i B. -i C. 0 D. 1

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2. The modulus of the complex number 3 + 4i is

A. 3 B. 4 C. 5 D. 7

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3. The conjugate of the complex number z = 2 - 5i is

A. 2 + 5i B. 2 - 5i C. -2 + 5i D. -2 - 5i

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4. If z = 1 + i, then |z|^2 is equal to

A. 1 B. 2 C. 3 D. 4

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5. The polar form of 1 + i is

A. √2(cos π/4 + i sin π/4) B. √2(cos π/2 + i sin π/2) C. 1(cos π/4 + i sin π/4) D. √2(cos π/6 + i sin π/6)

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6. If α and β are roots of the quadratic equation x^2 - 5x + 6 = 0, then α + β is

A. 3 B. 5 C. 6 D. 0

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7. The discriminant of the quadratic equation x^2 - 4x + 5 = 0 is

A. 0 B. -4 C. 4 D. -16

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8. The equation x^2 + 1 = 0 has roots

A. ±1 B. 0 C. ±i D. no roots

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9. If z = x + iy and |z| = 5, then x^2 + y^2 is equal to

A. 1 B. 5 C. 25 D. 10

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10. The number of distinct roots of the equation z^3 - 1 = 0 is

A. 1 B. 2 C. 3 D. 0

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11. The sum of the roots of the quadratic equation 2x^2 - 3x + 1 = 0 is

A. 2/3 B. 3/2 C. 3 D. -3/2

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12. The product of the roots of the quadratic equation 3x^2 - 5x + 2 = 0 is

A. 5 B. 2 C. 3/2 D. 2/3

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13. The cube roots of unity are

A. 1, ω, ω^2 B. -1, ω, ω^2 C. 1, i, -i D. 1, -1, i

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14. If z = 4(cos π/3 + i sin π/3), then Re(z) is

A. 2 B. 3 C. 4 D. 1

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15. If z1 = 1 + i and z2 = 1 - i, then z1 * z2 is

A. 2i B. 1 C. 2 D. -1

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16. The quadratic equation x^2 + 6x + 9 = 0 has

A. two distinct roots B. no real roots C. repeated roots D. complex roots

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17. If ω is a cube root of unity, then 1 + ω + ω^2 is

A. 1 B. -1 C. 0 D. 2

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18. If z1 = 2 + 3i and z2 = 4 - i, then z1 + z2 is

A. 6 + 2i B. 2 + 2i C. 6 - 2i D. 6 + 4i

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19. The roots of the quadratic equation x^2 + px + q = 0 are real and equal if

A. p^2 < 4q B. p^2 > 4q C. p^2 = 4q D. p^2 ≤ 4q

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20. If z = 2 - 3i, then the argument of z is

A. π/3 B. π/4 C. -π/3 D. -π/4