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Suppose (Zn)-1 CC and for each n € N+, let zn = xn+iyn, where an, yn E R. Suppose z = x+iy, with r, y R. Consider the following claim: If Zn → z, then xnx and yn →y. (8.1) Is the claim (1) above true? Provide a proof or counter-example to justify your answer. (8.2) What is the converse of the claim made in (1)? (8.3) Is the converse of the claim made in (1) true? Provide a proof or counter-example to justify your answer.

Suppose (Zn)-1 CC and for each n € N+, let zn = xn+iyn, where an, yn E R. Suppose z = x+iy, with r, y R. Consider the following claim: If Zn → z, then xnx and yn →y. (8.1) Is the claim (1) above true? Provide a proof or counter-example to justify your answer. (8.2) What is the converse of the claim made in (1)? (8.3) Is the converse of the claim made in (1) true? Provide a proof or counter-example to justify your answer.

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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Suppose (n)-1 CC and for each n € N+, let zn = xn+iyn, where xn, yn E R. Suppose z = x+iy, with x, y R. Consider the following claim: If znz, then xnx and yn →y. (8.1) Is the claim (1) above true? Provide a proof or counter-example to justify your answer. (8.2) What is the converse of the claim made in (1)? (8.3) Is the converse of the claim made in (1) true? Provide a proof or counter-example to justify your answer.
Transcribed Image Text:Suppose (n)-1 CC and for each n € N+, let zn = xn+iyn, where xn, yn E R. Suppose z = x+iy, with x, y R. Consider the following claim: If znz, then xnx and yn →y. (8.1) Is the claim (1) above true? Provide a proof or counter-example to justify your answer. (8.2) What is the converse of the claim made in (1)? (8.3) Is the converse of the claim made in (1) true? Provide a proof or counter-example to justify your answer.
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