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If z = x + iy is a complex number with x, y E R, we define the complex conjugate of z by z = x – iy. (a) What is the geometric interpretation of Zz? (b) Show that |z|² = zz. (c) Prove that if z belongs to the unit circle, then 1/z = z.

If z = x + iy is a complex number with x, y E R, we define the complex conjugate of z by z = x – iy. (a) What is the geometric interpretation of Zz? (b) Show that |z|² = zz. (c) Prove that if z belongs to the unit circle, then 1/z = z.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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If z = x + iy is a complex number with x, y ∈ R, we define the complex conjugate of z by ¯z = x − it.

(a) What is the geometric interpretation of ¯z?

(b) Show that |z| 2 = zz¯.

(c) Prove that if z belongs to the unit circle, then 1/z = ¯z. 

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If z = x + iy is a complex number with x, y E R, we define the complex conjugate of z by z = x – iy. (a) What is the geometric interpretation of z? (b) Show that |z|2 = zz. (c) Prove that if z belongs to the unit circle, then 1/z = Z. -
Transcribed Image Text:If z = x + iy is a complex number with x, y E R, we define the complex conjugate of z by z = x – iy. (a) What is the geometric interpretation of z? (b) Show that |z|2 = zz. (c) Prove that if z belongs to the unit circle, then 1/z = Z. -
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