You have complex numbers Z₁ = e³-14, z2 = √√3+2i, 23 = = 3-1/2/³ 1. Write Z₁ in classical form z = x + iy; reio; 2. Write Z2, Z3 in exponential form z = 3. Write Z₁, Z2, Z3 in trigonometric form z = r(cos + i sin 0); 4. Make operations between the complex numbers Z3 - |Z₁ + Z2, Z2 * Z3, Z = Re(z₁ * Z2), Im(z2 — Z3) Z₂' 5. Find the 3 roots of number Z3; 6. Find the number (z₁);
You have complex numbers Z₁ = e³-14, z2 = √√3+2i, 23 = = 3-1/2/³ 1. Write Z₁ in classical form z = x + iy; reio; 2. Write Z2, Z3 in exponential form z = 3. Write Z₁, Z2, Z3 in trigonometric form z = r(cos + i sin 0); 4. Make operations between the complex numbers Z3 - |Z₁ + Z2, Z2 * Z3, Z = Re(z₁ * Z2), Im(z2 — Z3) Z₂' 5. Find the 3 roots of number Z3; 6. Find the number (z₁);
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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Question
A needed for all parts please do correctly in 30 minutes and get the thumbs up please show me neat and clean work for it
Transcribed Image Text:A)
You have complex numbers Z₁ =
= e³-i², Z2 = √√3+2i, 23 =
B)
1. Write Z₁ in classical form z = x + iy;
2. Write Z2, Z3 in exponential form z = reiº ;
3. Write Z₁, Z2, Z3 in trigonometric form z= r(cos+ i sin 0);
4. Make operations between the complex numbers
Z3
|Z₁ + Z₂, Z2 * Z3, Z =
Z₂
5. Find the 3 roots of number Z3;
6. Find the number (Z₁)6;
"
-
Re(z₁ * Z₂), Im(Z2 — Z3)
Compute the following limit if it exist lim
Z→-i
√√3
گیز
z5-42z
C)
Write the following function f(z) = z²³ − z + 1 in form f(z) = u(x; y) + iv(x; y)
(find the real and imaginary part of complex function Re(ƒ(z)) = u(x; y),
Im(f(z)) = v(x; y))
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