1.1 Let z,w in C. Show that absolute value of (z + w)2 + absolute value of (z - w)2 = 2(absolute value of z2 + absolute value of w2).1.2 Determine if the following statement is true or false. Motivate your answer.If Re(z) > Re(w) and Im(z) > Im(w), then absolute value of z > absolute value of w.

Answered: Let z,w in C. Show that absolute value…

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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1.1 Let z,w in C. Show that absolute value of (z + w)² + absolute value of (z - w)² = 2(absolute value of z² + absolute value of w²).

1.2 Determine if the following statement is true or false. Motivate your answer.
If Re(z) > Re(w) and Im(z) > Im(w), then absolute value of z > absolute value of w.

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Consider two complex numbers $z_{1}$ and $z_{2}$ . Then ${|z_{1} + z_{2}|}^{2} = {|z_{1}|}^{2} + {|z_{2}|}^{2} + 2 Re (z_{1} z_{2})$ .