Class 11 Math - Complex Numbers - MERIT YARD
Class 11 Math - Complex Numbers - MERIT YARD
1 / 40What is the value of
\( i \)?
A) \( -1 \)
B) \( \sqrt{-1} \)
C) \( 1 \)
D) \( 0 \)
2 / 40Find the exact value of
\( i^2 \).
A) \( -1 \)
B) \( 1 \)
C) \( i \)
D) \( -i \)
3 / 40Find the exact value of
\( i^3 \).
A) \( i \)
B) \( 1 \)
C) \( -i \)
D) \( -1 \)
4 / 40Find the exact value of
\( i^4 \).
A) \( i \)
B) \( -i \)
C) \( -1 \)
D) \( 1 \)
5 / 40For the complex number \( z = 3 + 4i \).
What is its real part?
A) \( 4 \)
B) \( 3i \)
C) \( 3 \)
D) \( 4i \)
6 / 40For the complex number \( z = 3 + 4i \).
What is its imaginary part?
A) \( 3 \)
B) \( 3i \)
C) \( 4i \)
D) \( 4 \)
7 / 40What is the conjugate of the complex number
\( z = x + iy \)?
A) \( x - iy \)
B) \( x + iy \)
C) \( -x + iy \)
D) \( -x - iy \)
8 / 40Find the conjugate of
\( z = 2 + 3i \).
A) \( -2 - 3i \)
B) \( 2 - 3i \)
C) \( 2 + 3i \)
D) \( -2 + 3i \)
9 / 40What is the modulus of the complex number
\( z = x + iy \)?
A) \( x^2 + y^2 \)
B) \( x + y \)
C) \( x^2 - y^2 \)
D) \( \sqrt{x^2 + y^2} \)
10 / 40Find the modulus of
\( z = 3 + 4i \).
A) \( 7 \)
B) \( 25 \)
C) \( 5 \)
D) \( \sqrt{7} \)
11 / 40Add the complex numbers:
\( (2 + 3i) + (1 + i) \)
A) \( 3 + 3i \)
B) \( 3 + 4i \)
C) \( 2 + 4i \)
D) \( 4 + 4i \)
12 / 40Subtract the complex numbers:
\( (5 + 4i) - (2 + i) \)
A) \( 3 + 3i \)
B) \( 3 + 5i \)
C) \( 7 + 5i \)
D) \( 7 + 3i \)
13 / 40Evaluate the product:
\( i \times i \)
A) \( i \)
B) \( 1 \)
C) \( -1 \)
D) \( -i \)
14 / 40Find the exact value of
\( i^{10} \).
A) \( i \)
B) \( 1 \)
C) \( -i \)
D) \( -1 \)
15 / 40Find the exact value of
\( i^{11} \).
A) \( -i \)
B) \( i \)
C) \( 1 \)
D) \( -1 \)
16 / 40Find the exact value of
\( i^{12} \).
A) \( -1 \)
B) \( 1 \)
C) \( i \)
D) \( -i \)
17 / 40If \( z = 0 + ib \), then the complex number is called:
A) Purely real
B) Irrational
C) Rational
D) Purely imaginary
18 / 40If \( z = a + 0i \), then the complex number is called:
A) Purely imaginary
B) Irrational
C) Purely real
D) Integer
19 / 40What is the multiplicative inverse of
\( i \)?
A) \( -i \)
B) \( i \)
C) \( 1 \)
D) \( -1 \)
20 / 40For any complex number \( z \), the product
\( z \bar{z} \) is equal to:
A) \( z^2 \)
B) \( |z|^2 \)
C) \( 0 \)
D) \( 1 \)
21 / 40Find the conjugate of the complex number
\( z = 1 + i \).
A) \( -1 - i \)
B) \( 1 + i \)
C) \( -1 + i \)
D) \( 1 - i \)
22 / 40Evaluate the expression:
\( \sqrt{-16} \)
A) \( -4 \)
B) \( 4 \)
C) \( 4i \)
D) \( -4i \)
23 / 40Evaluate the expression:
\( \sqrt{-25} \)
A) \( 5 \)
B) \( 5i \)
C) \( -5 \)
D) \( -5i \)
24 / 40What is the value of
\( \frac{1}{i} \)?
A) \( -i \)
B) \( i \)
C) \( 1 \)
D) \( -1 \)
25 / 40Find the exact value of
\( i^{100} \).
A) \( i \)
B) \( -1 \)
C) \( 1 \)
D) \( -i \)
26 / 40Find the exact value of
\( i^{-1} \).
A) \( 1 \)
B) \( -1 \)
C) \( i \)
D) \( -i \)
27 / 40What are the solutions of the equation
\( x^2 + 1 = 0 \)?
A) \( \pm 1 \)
B) \( \pm i \)
C) \( 1, i \)
D) \( 0 \)
28 / 40What are the solutions of the equation
\( x^2 + 4 = 0 \)?
A) \( \pm 2i \)
B) \( \pm 2 \)
C) \( 2i \)
D) \( -2i \)
29 / 40Add the complex numbers:
\( (a + ib) + (c + id) \)
A) \( ac + ibd \)
B) \( (a + d) + i(b + c) \)
C) \( a + c + b + d \)
D) \( (a + c) + i(b + d) \)
30 / 40If two complex numbers are equal, \( a + ib = c + id \), then:
A) \( a = d, b = c \)
B) \( a = b, c = d \)
C) \( a = c, b = d \)
D) \( ac = bd \)
31 / 40Find the value of
\( i^5 \).
A) \( -i \)
B) \( 1 \)
C) \( -1 \)
D) \( i \)
32 / 40What is the modulus of
\( z = 1 + i \)?
A) \( 2 \)
B) \( \sqrt{2} \)
C) \( 1 \)
D) \( 0 \)
33 / 40What is the modulus of
\( z = -i \)?
A) \( 1 \)
B) \( -1 \)
C) \( 0 \)
D) \( i \)
34 / 40Find the conjugate of
\( z = -3i \).
A) \( -3 \)
B) \( 3 \)
C) \( 3i \)
D) \( -3i \)
35 / 40The set of all complex numbers is mathematically denoted by:
A) \( \mathbb{C} \)
B) \( \mathbb{R} \)
C) \( \mathbb{Z} \)
D) \( \mathbb{Q} \)
36 / 40The complex number system is an extension of which number system?
A) Integers
B) Real numbers \( \mathbb{R} \)
C) Whole numbers
D) Natural numbers
37 / 40Expand and simplify:
\( (1 + i)^2 \)
A) \( 2 \)
B) \( -2i \)
C) \( 2i \)
D) \( 0 \)
38 / 40Expand and simplify:
\( (1 - i)^2 \)
A) \( 2 \)
B) \( 2i \)
C) \( 0 \)
D) \( -2i \)
39 / 40Find \( x \) if:
\( x + 2i = 3 + 2i \)
A) \( 3 \)
B) \( 2 \)
C) \( 0 \)
D) \( 5 \)
40 / 40Find \( y \) if:
\( 4 + yi = 4 - 5i \)
A) \( 5 \)
B) \( -5 \)
C) \( 4 \)
D) \( 0 \)
Test Analysis

Correct ✅ 0

Wrong ❌ 0

Unattempted ⚠️ 40

Accuracy 🎯 0%

Time Taken ⏱️ 00m 00s

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