Math Problem Statement

Let z

4 + 1 i

Calculate ¯ z (i.e., the complex conjugate of z )

Solution

Given the complex number z=4+1iz = 4 + 1i, its complex conjugate z\overline{z} is obtained by changing the sign of the imaginary part.

So, the complex conjugate z\overline{z} is:

z=41i\overline{z} = 4 - 1i

Would you like any further details or explanations on complex conjugates?

Here are 5 related questions you might find useful:

  1. What is the modulus of the complex number z=4+1iz = 4 + 1i?
  2. How do you find the argument of a complex number?
  3. What happens if you multiply a complex number by its conjugate?
  4. Can you add and subtract complex numbers? How does it work?
  5. How are complex numbers used in real-world applications?

Tip: The product of a complex number and its conjugate always results in a real number.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Complex Numbers
Conjugates

Formulas

Complex conjugate formula: For z = a + bi, z̅ = a - bi

Theorems

Properties of complex conjugates: z * z̅ = a^2 + b^2

Suitable Grade Level

Grades 9-12