BE SURE TO EXPLAIN EVERYTHING! Consider the two complex numbers z₁ = ein/4 and Z₂ = ei³π/4Plot Z₁, Z2, Z₁, and z2 in the complex plane and label them.Calculate Z₁Z2, Z2/2₁, and z₂z₁ using the polar forms given. Simplify your answers.Write z₁ and 2₂ in the Cartesian form a+bi, then calculate their product Z₁ Z₂ using yourresults.

The two complex numbers are as follows:Find: the complex plane.b) using polar form.c) Write in…

Answered: Consider the two complex numbers 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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Related questions

Question

BE SURE TO EXPLAIN EVERYTHING!

Consider the two complex numbers z₁ = ein/4 and Z₂ = ei³π/4
Plot Z₁, Z2, Z₁, and z2 in the complex plane and label them.
Calculate Z₁Z2, Z2/2₁, and z₂z₁ using the polar forms given. Simplify your answers.
Write z₁ and 2₂ in the Cartesian form a+bi, then calculate their product Z₁ Z₂ using your
results.

Expert Solution

Step 1: Write the given information:

The two complex numbers are as follows:

$z subscript 1 equals e to the power of i straight pi over 4 end exponent space comma space z subscript 2 equals e to the power of i fraction numerator 3 straight pi over denominator 4 end fraction end exponent$

Find:

$z subscript 1 space comma space z subscript 2 space comma space z subscript 1 asterisk times space comma space z subscript 2 asterisk times$ the complex plane.

b) $z subscript 1 z subscript 2 space comma space z subscript 2 divided by z subscript 1 space comma space z subscript 2 z subscript 1 asterisk times$ using polar form.

c) Write $z subscript 1$ $z subscript 2$ in Cartesian form.

d) Product number using Cartesian form.