Education
Class 10 Math Chapter wise Test 2 | Complex Numbers Chapter 1 pdf download
Class 10 Math Unit 1 Test 2
Class 10 Math Chapter 1 Complex Numbers Test PDF Exercise No. 1.1 and Exercise No. 1.2 is provided here for students preparing for their Class 10 Mathematics exams. This Complex Numbers Chapter 1 Test includes objective-type MCQs, short-answer questions, and subjective questions covering important concepts from Unit 1. Students can use this Class 10 Math Unit Wise Test for classroom practice, revision, and exam preparation.
Unit Wise Class Test
T-2
Unit 1: Complex Numbers
Time: 5 minutes
(Objective Type)
Total Marks: 5
1. Tick the correct answer.(1 × 5 = 5)
(i) i7 =
i⁷ = i⁴ · i³ = (1)(i²· i) = (−1)(i) = −i Ans: (d)
(ii) 1i =
Multiply top and bottom by i: 1 × ii × i = ii² = i−1 = −i Ans: (a)
(iii) Solutions of the equation x2 + 1 = 0 is / are:
x² = −1 → x = ±√−1 = ± i
So x = i and x = −i Ans: (d)
So x = i and x = −i Ans: (d)
(iv) i−3 =
i−3 = 1i³ = 1−i
Multiply top and bottom by i: i−i² = i1 = i Ans: (b)
Multiply top and bottom by i: i−i² = i1 = i Ans: (b)
(v) 2 − √−4 =
√−4 = √4 · √−1 = 2i
2 − 2i Ans: (b)
2 − 2i Ans: (b)
Unit Wise Class Test
T-2
Unit 1: Complex Numbers
Time: 35 minutes
(Subjective Type)
Total Marks: 20
2. Write short answers to the following questions:(6 × 2 = 12)
(i) Simplify: i−25
Step 1: i−25 = 1i²⁵
Step 2: i²⁵ = i²⁴ · i = (i⁴)⁶ · i = (1)(i) = i
Step 3: 1i = ii² = i−1 = −i
Ans: −i
Step 2: i²⁵ = i²⁴ · i = (i⁴)⁶ · i = (1)(i) = i
Step 3: 1i = ii² = i−1 = −i
Ans: −i
(ii) Write in terms of i, if 25 + √−165
Step 1: √−16 = √16 · √−1 = 4i
Step 2: Expression = 25 + 4i5
Ans: 2 + 4i5 = 25 + 45i
Step 2: Expression = 25 + 4i5
Ans: 2 + 4i5 = 25 + 45i
(iii) Find the values of x and y, if (2x + 5) + (y − 3)i = 1 + 2i
Step 1: Equate real parts: 2x + 5 = 1 → 2x = −4 → x = −2
Step 2: Equate imaginary parts: y − 3 = 2 → y = 5
Ans: x = −2, y = 5
Step 2: Equate imaginary parts: y − 3 = 2 → y = 5
Ans: x = −2, y = 5
(iv) Add (3 + 4i) and (5 − 2i).
Step 1: (3 + 4i) + (5 − 2i) = (3 + 5) + (4 − 2)i
Ans: 8 + 2i
Ans: 8 + 2i
(v) Write additive inverse for each complex number: 3 + 2i
Additive inverse of z is −z, since z + (−z) = 0.
For 3 + 2i: −(3 + 2i) = −3 − 2i
Check: (3 + 2i) + (−3 − 2i) = 0 ✓
Ans: −3 − 2i
For 3 + 2i: −(3 + 2i) = −3 − 2i
Check: (3 + 2i) + (−3 − 2i) = 0 ✓
Ans: −3 − 2i
(vi) Find multiplicative inverse for each complex number: 4 + 5i
Step 1: Multiplicative inverse of z is 1z = 14 + 5i
Step 2: Multiply top and bottom by conjugate (4 − 5i): 4 − 5i(4 + 5i)(4 − 5i)
Step 3: Denominator = 4² − (5i)² = 16 + 25 = 41
Ans: 4 − 5i41 = 441 − 541i
Step 2: Multiply top and bottom by conjugate (4 − 5i): 4 − 5i(4 + 5i)(4 − 5i)
Step 3: Denominator = 4² − (5i)² = 16 + 25 = 41
Ans: 4 − 5i41 = 441 − 541i
Note: Answer the following Questions.(4 + 4 = 8)
3. Simplify: 1 + 2i3 − i (2 + i)
Step 1: Multiply numerators: (1 + 2i)(2 + i) = 2 + i + 4i + 2i² = 2 + 5i − 2 = 5i
Step 2: Expression = 5i3 − i
Step 3: Multiply top and bottom by conjugate (3 + i): 5i(3 + i)(3 − i)(3 + i)
Step 4: Numerator: 15i + 5i² = 15i − 5 = −5 + 15i. Denominator: 9 − i² = 9 + 1 = 10
Step 5: −5 + 15i10 = −12 + 32i
Ans: −12 + 32i
Step 2: Expression = 5i3 − i
Step 3: Multiply top and bottom by conjugate (3 + i): 5i(3 + i)(3 − i)(3 + i)
Step 4: Numerator: 15i + 5i² = 15i − 5 = −5 + 15i. Denominator: 9 − i² = 9 + 1 = 10
Step 5: −5 + 15i10 = −12 + 32i
Ans: −12 + 32i
4. Simplify: (5 + 2i) ÷ (6 − 3i)
Step 1: Write as fraction: 5 + 2i6 − 3i
Step 2: Multiply top and bottom by conjugate (6 + 3i): (5 + 2i)(6 + 3i)(6 − 3i)(6 + 3i)
Step 3: Numerator: 30 + 15i + 12i + 6i² = 30 + 27i − 6 = 24 + 27i
Step 4: Denominator: 36 − 9i² = 36 + 9 = 45
Step 5: 24 + 27i45 = 2445 + 2745i = 815 + 35i
Ans: 815 + 35i
Step 2: Multiply top and bottom by conjugate (6 + 3i): (5 + 2i)(6 + 3i)(6 − 3i)(6 + 3i)
Step 3: Numerator: 30 + 15i + 12i + 6i² = 30 + 27i − 6 = 24 + 27i
Step 4: Denominator: 36 − 9i² = 36 + 9 = 45
Step 5: 24 + 27i45 = 2445 + 2745i = 815 + 35i
Ans: 815 + 35i
