Math Problem Statement

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

Solution

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

Let's examine each option:

a. 3i3i: This is purely imaginary, with b=3b = 3.

b. i3-i \sqrt{3}: This is also imaginary, with b=3b = -\sqrt{3}.

c. 33: This is purely real, with no imaginary component, so b=0b = 0.

d. 3\sqrt{-3}: This is equal to i3i\sqrt{3}, making it purely imaginary with b=3b = \sqrt{3}.

Thus, the correct answer is:

c. 3

Would you like more details or have any other questions?


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.

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Math Problem Analysis

Mathematical Concepts

Complex Numbers
Real and Imaginary Parts

Formulas

z = a + bi (General form of a complex number)

Theorems

Identification of purely real or imaginary numbers in the complex plane

Suitable Grade Level

Grades 10-12