Mathematics Unit 01 Chapter Wise Class Test 1 – Complex Numbers

Chapter Wise Class Test – Test #1

This Mathematics Chapter Wise Class Test is based on Unit 01: Complex Numbers. The test contains objective and subjective questions and is designed for classroom practice and preparation.

Test Information

• Subject: Mathematics
• Unit: 01
• Test: Chapter Wise Class Test – Test #1
• Total Time: 35 Minutes
• Total Marks: 25
• Objective Time: 10 Minutes
• Objective Marks: 8
• Subjective Time: 25 Minutes
• Subjective Marks: 17

Objective – Q.1

Time: 10 Minutes | Marks: 8

Note: Four possible answers A, B, C and D to each question are given. The choice which you think is correct, fill that circle in front of that question with Marker or Pen ink. Cutting or filling two or more circles will result in zero mark in that question.

Multiple Choice Questions

1. Imaginary part of (2 − i)(2 + i) is:
   • (A) 0
   • (B) 1
   • (C) 7
   • (D) 9
2. x + iy will be pure imaginary number, when:
   • (A) y = 0
   • (B) x = 0
   • (C) i = 0
   • (D) x = 0, y = 0
3. If z = 4 + 4i, then z + z̄ =
   • (A) 8
   • (B) 8 + 8i
   • (C) 8i
   • (D) 0
4. If z = 5 + 4i, then |z| =
   • (A) 9
   • (B) 25
   • (C) 41
   • (D) √41
5. If 2a + (b − 1)i = 10 + 4i then a = ______.
   • (A) 5
   • (B) 10
   • (C) 2a + 10
   • (D) 2a − 10
6. The additive inverse of (7 − 2i) is:
   • (A) (−2 + 7i)
   • (B) (−7 − 2i)
   • (C) (0, 0)
   • (D) (−7 + 2i)
7. What is the conjugate of −4 + 4i?
   • (A) 4 − 4i
   • (B) −4 + 4i
   • (C) −8i
   • (D) −4 − 4i
8. If z = −√3 − √5i then |z| =
   • (A) 8
   • (B) √34
   • (C) √3 + √5
   • (D) √8i

Subjective

Time: 25 Minutes | Marks: 17

Part – I

Q.2: Write short answers to the following questions.

(6 × 2 = 12)

1. What is the result of multiplying a complex number by its conjugate?
2. Simplify: i³⁷
3. Find additive and multiplicative inverse of z = 8 + 9i.
4. What is a “pure imaginary” number?
5. If z = 1 − 2yi then find −3z.
6. Write the Associative property for multiplication of complex numbers.

Part – II

Note: Attempt the following question.

Q.3: Find real and imaginary parts of

z = ((4 + 3i) / (3 + 2i))⁻¹

Marks: 5

Important Topics Covered

• Complex numbers
• Real and imaginary parts
• Pure imaginary numbers
• Complex conjugates
• Modulus of a complex number
• Additive inverse
• Multiplicative inverse
• Powers of i
• Properties of complex numbers

Answer Key – Objective

Solution of Q.3

Given:

z = ((4 + 3i) / (3 + 2i))⁻¹

Therefore,

z = (3 + 2i) / (4 + 3i)

Rationalizing the denominator:

z = [(3 + 2i)(4 − 3i)] / [(4 + 3i)(4 − 3i)]

On simplifying:

z = (18 − i) / 25

Hence,

Real part = 18/25

Imaginary part = −1/25

This chapter-wise class test can be used for classroom assessment, revision, homework, test preparation and practice of complex numbers.

Keywords: Mathematics Class Test, Unit 01 Mathematics, Complex Numbers Test, Complex Numbers MCQs, Chapter Wise Test, Mathematics Objective Questions, Mathematics Subjective Questions, Complex Numbers MCQs with Answers, Class Test Mathematics