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 , where is the real part and is the imaginary part. To identify which of the given complex numbers has , we need to find which number does not have an imaginary component.
Let's examine each option:
a. : This is purely imaginary, with .
b. : This is also imaginary, with .
c. : This is purely real, with no imaginary component, so .
d. : This is equal to , making it purely imaginary with .
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:
- What is the real part of a complex number?
- How do you add two complex numbers?
- What is the modulus of a complex number?
- How do you represent complex numbers on the complex plane?
- 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