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Punjab (PTB) · Chapter test · Free

1st Year Mathematics Chapter 1 TestUNIT 1: Complex Numbers

30 marks · 40 minutes · 21 questions. Covers: UNIT 1: Complex Numbers.

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1st Year Mathematics Chapter 1 Test

1st Year · Mathematics · Punjab (PTB)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 30Time: 40 minutes

Q1. Multiple choice questions (Attempt all · 10 × 1 = 10)

  1. Multiplicative inverse of (1,0) is:

    1. (-1,0)

    2. (0,1)

    3. (0,-1)

    4. (1,0)

  2. If 

    1. -2-3

    2. 2-3

    3. -2+3

    4. 2+3

  3. If Z is complex number, then  is:

    1. Z2

  4. For a complex number (0,1)i = ......

    1. (1,0)

    2. (-1,0)

    3. (0,1)

    4. (0,-1)

  5. If 

    1. Z1 < Z2

    2. Z1 > Z2

  6. Argument  is:

    1. 60o

    2. 30o

    3. 45o

    4. 90o

  7. For any  is equivalent to ......:

  8. Polar form of complex number 

  9. If  is the cube root of unity then 

    1. 256

    2. -256

    3. -256

    4. 256

  10. A complex number  can also be expressed as:

Q2. Short questions (Attempt any 6 of 8 · 6 × 2 = 12)

  1. If then find: z1+z2

  2. If then find the following and express the result into x+y form: z1+z2

  3. Find the product of .

  4. Solve the following equation: z3-5z2+z-5=0

  5. Plot the following points:

  6. Find the three cube roots of: -125

  7. If , then evaluate the following:

  8. Solve the following equation: z3+z2+z+1=0

Q3. Long questions (Attempt any 2 of 3 · 2 × 4 = 8)

  1. Evaluate:

  2. If is an imaginary cube root of unity, prove that

  3. If is a cube root of unity, prove that