Find the multiplicative inverse of following complex number? (-8,0)

To find the multiplicative inverse of a complex number, we use the formula:

\[
z^{-1} = \frac{1}{z}
\]

For a complex number \( z = a + bi \), its multiplicative inverse is:

\[
z^{-1} = \frac{a - bi}{a^2 + b^2}
\]

Given the complex number \( z = -8 + 0i \), the inverse would be:

\[
z^{-1} = \frac{-8 - 0i}{(-8)^2 + 0^2} = \frac{-8}{64} = -\frac{1}{8}
\]

So, the multiplicative inverse of \( (-8, 0) \) is \( \left(-\frac{1}{8}, 0\right) \).

Would you like any further explanation or have any questions?

Here are 5 related questions:

1. What is the multiplicative inverse of \( (2, 3) \)?
2. How do you find the conjugate of a complex number?
3. What is the modulus of a complex number, and how is it calculated?
4. Can a real number be considered a complex number?
5. What is the significance of the complex plane in mathematics?

**Tip:** The multiplicative inverse of a complex number is also known as the reciprocal.

Discover how to find the multiplicative inverse of the complex number (-8, 0) using step-by-step calculations. Learn about complex numbers, the formula for multiplicative inverse, and its application in mathematics. Suitable for Grades 10-12 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation