Please show work in detail. 2. Find z1 Z2. Let z110 (cos 플 +i sin ).z2 = 2 (cos + i sin ).line

Name: Please show work in detail. 2. Find z1 Z2. Let z110 (cos 플 +i sin ).z2
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Description: Please show work in detail. 2. Find z1 Z2. Let z110 (cos 플 +i sin ).z2 = 2 (cos + i sin ).line

Given z1=10cos 11π12+i sin 11π12 and z2=2cos 5π4+i sin 5π4. Find z1z2.

Answered: Find z1 Z2. Let z1 ti sin z2 = 2 (cos +…

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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Please show work in detail.

2. Find z1 Z2. Let z1
10 (cos 플 +i sin ).
z2 = 2 (cos + i sin ).
line

Expert Solution

Step 1

Given $z_{1} = 10 (\cos \frac{11 π}{12} + i \sin \frac{11 π}{12}) a n d z_{2} = 2 (\cos \frac{5 π}{4} + i \sin \frac{5 π}{4})$ .

Find $z_{1} z_{2}$ .

Step 2

By using the Euler's formula $e^{i x} = \cos x + i \sin x$ , write $z_{1} a n d z_{2}$ as

$z_{1} = 10 e^{i \frac{11 π}{12}} a n d z_{2} = 2 e^{i \frac{5 π}{4}}$

Therefore,

$z_{1} z_{2} = 10 e^{i \frac{11 π}{12}} \cdot 2 e^{i \frac{5 π}{4}} = 20 e^{i (\frac{11 π}{12} + \frac{5 π}{4})} = 20 e^{i \frac{26 π}{12}} = 20 e^{i \frac{13 π}{6}}$

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