Use z=a+b i to show that z̅=z

Name: Problem 93, Chapter 1: Algebra and Trigonometry
Uploaded: 2021-04-11T19:03:39-08:00
Duration: 1 min 40 s
Channel: Dharmendra Jain
Description: Use z=a+b i to show that z̅=z

step 1 Hello everyone, so in this one question we have a complex number jad equals to a plus b aorta an

Question

Use $z=a+b i$ to show that $\overline{\bar{z}}=z$

   Use $z=a+b i$ to show that $\overline{\bar{z}}=z$

Algebra and Trigonometry

Michael Sullivan 11th Edition

Chapter 1, Problem 93

Instant Answer

Solved by Expert Dharmendra Jain

04/11/2021

Step 1

If $z=a+bi$ is a complex number, then the conjugate of $z$, denoted by $\bar{z}$, is given by $a-bi$. Show more…

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Use $z=a+b i$ to show that $\overline{\bar{z}}=z$

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Key Concepts

Complex Numbers

Complex numbers are numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit with the property that i² = -1. They provide a way to extend the real numbers into a two-dimensional number system, useful in many areas of mathematics and engineering.

Complex Conjugate

The complex conjugate of a complex number a + bi is defined as a - bi. This operation reflects the complex number across the real axis in the complex plane and is instrumental in various operations, such as simplifying division of complex numbers and finding moduli.

Involution

An involution is a function that, when applied twice, returns the original input. In the context of complex numbers, taking the complex conjugate twice (i.e., conjugating the conjugate) results in the original number, demonstrating that complex conjugation is an involution.

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