Complex Conjugates The complex conjugate of is . Let . (a) Prove that . (b) Use the
Chapter 6, Problem 6.1.1.481(choose chapter or problem)
Complex Conjugates The complex conjugate of \(z=a+b i \text { is } \bar{z}=a-b i \text {. Let } z=r(\cos \theta+i \sin \theta)\).
(a) Prove that \(\bar{z}=r[\cos (-\theta)+i \sin (-\theta)]\).
(b) Use the trigonometric form to find \(z \cdot \bar{z}\).
(c) Use the trigonometric form to find \(z / \bar{z} \text {, if } \bar{z} \neq 0\).
(d) Prove that \(-z=r[\cos (\theta+\pi)+i \sin (\theta+\pi)]\).
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