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Consider the two complex numbers Z₁ = ein/4 and Z₂ = e²³π/4 Plot Z₁, Z2, Z₁, and z2 in the complex plane and label them. Calculate Z₁ Z2, Z₂/Z₁, and z₂z₁ using the polar forms given. Simplify your answers. Write z₁ and Z₂ in the Cartesian form a+bi, then calculate their product Z₁ Z₂ using your results. Check your answer with the result you obtained in part (b).

Consider the two complex numbers Z₁ = ein/4 and Z₂ = e²³π/4 Plot Z₁, Z2, Z₁, and z2 in the complex plane and label them. Calculate Z₁ Z2, Z₂/Z₁, and z₂z₁ using the polar forms given. Simplify your answers. Write z₁ and Z₂ in the Cartesian form a+bi, then calculate their product Z₁ Z₂ using your results. Check your answer with the result you obtained in part (b).

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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Help me with this problem, assuming I have no prior knowledge of complex numbers.

Consider the two complex numbers z₁ = eiñ/4 and Z₂ = ei³¹/4 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. Check your answer with the result you obtained in part (b).
Transcribed Image Text:Consider the two complex numbers z₁ = eiñ/4 and Z₂ = ei³¹/4 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. Check your answer with the result you obtained in part (b).
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