Operations and Properties of Complex Numbers Quiz

Test your understanding of complex numbers with questions on modulus, conjugate, product, quotient, real & imaginary parts.

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What is the modulus of the complex number 3 + 4i?

What is the conjugate of the complex number 2 - 3i?

2 - 3i

2 + 3i

-2 - 3i

-2 + 3i

What is the modulus of the complex number (-3 + 4i)?

What is the modulus of the complex number (-5 - 12i)?

√169

What is the modulus of the complex number (1 - i)?

√2

√5

Which of the following is true about the product of two complex conjugates?

Always a real number

Always a complex number

Always an imaginary number

Depends on the complex numbers involved

What is the square of the complex number 1 + i?

1 + i

1 - i

2 + 2i

What is the argument (angle) of the complex number -1 + √3i in radians?

π/6

π/3

π/4

π/2

Which of the following is NOT a property of complex conjugates?

The product of a complex number and its conjugate is always real.

The sum of a complex number and its conjugate is always real.

The product of two complex conjugates is always a complex number.

The difference of a complex number and its conjugate is always imaginary.

#10

What is the product of the complex numbers (2 + i) and (3 - 2i)?

4 + 5i

4 + i

3 + 7i

7 - i

#11

If z = 2 + 3i and w = 4 - 2i, what is the product zw?

2 + 10i

8 + 2i

14 + 4i

4 + 8i

#12

If z = 3 - 2i and w = -1 + 4i, what is the quotient z/w?

0.5 - 0.5i

0.5 + 0.5i

-0.5 - 0.5i

-0.5 + 0.5i

#13

What is the cube of the complex number 1 - i?

1 - i

1 + i

1 + 3i

2 - 2i

#14

If |z| = 5 and |w| = 3, what is |z - w|?

#15

If z = 2 + 3i and w = 1 - 2i, what is the difference z - w?

1 + 5i

1 + i

3 + 5i

3 + i

Operations and Properties of Complex Numbers Quiz

What is the modulus of the complex number 3 + 4i?

What is the conjugate of the complex number 2 - 3i?

What is the modulus of the complex number (-3 + 4i)?

What is the modulus of the complex number (-5 - 12i)?

What is the modulus of the complex number (1 - i)?

Which of the following is true about the product of two complex conjugates?

What is the square of the complex number 1 + i?

What is the argument (angle) of the complex number -1 + √3i in radians?

Which of the following is NOT a property of complex conjugates?

What is the product of the complex numbers (2 + i) and (3 - 2i)?

If z = 2 + 3i and w = 4 - 2i, what is the product zw?

If z = 3 - 2i and w = -1 + 4i, what is the quotient z/w?

What is the cube of the complex number 1 - i?

If |z| = 5 and |w| = 3, what is |z - w|?

If z = 2 + 3i and w = 1 - 2i, what is the difference z - w?

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