Which of the following complex numbers has b = 0? a. 3i b. -i square root of 3   c. 3 d. square root of -3

The general form of a complex number is \( z = a + bi \), where \( a \) is the real part and \( b \) is the imaginary part. To identify which of the given complex numbers has \( b = 0 \), we need to find which number does not have an imaginary component.

Let's examine each option:

a. \( 3i \): This is purely imaginary, with \( b = 3 \).

b. \( -i \sqrt{3} \): This is also imaginary, with \( b = -\sqrt{3} \).

c. \( 3 \): This is purely real, with no imaginary component, so \( b = 0 \).

d. \( \sqrt{-3} \): This is equal to \( i\sqrt{3} \), making it purely imaginary with \( b = \sqrt{3} \).

Thus, the correct answer is:

**c. 3**

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Here are 5 related questions to explore further:

1. What is the real part of a complex number?
2. How do you add two complex numbers?
3. What is the modulus of a complex number?
4. How do you represent complex numbers on the complex plane?
5. What is the conjugate of a complex number?

**Tip:** A purely real number is a special case of a complex number where the imaginary part is zero.

Which of the following complex numbers has b = 0? a. 3i b. -i square root of 3 c. 3 d. square root of -3

Learn how to identify complex numbers with zero imaginary parts using the general form z = a + bi. This problem explores concepts in complex numbers and is suitable for students in Grades 10-12.

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