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Category: Relation and Functions

z-2iz-3-3i-geometrical-representation-is-

Question Number 146041 by alcohol last updated on 10/Jul/21 $${z}'\:=\:\mathrm{2}{iz}\:+\:\left(\mathrm{3}−\mathrm{3}{i}\right) \\ $$$${geometrical}\:{representation}\:{is}? \\ $$ Answered by ajfour last updated on 10/Jul/21 $$\frac{{dx}}{{dt}}+{i}\frac{{dy}}{{dt}}=\mathrm{2}{i}\left({x}+{iy}\right)+\mathrm{3}\left(\mathrm{1}−{i}\right) \\ $$$$\Rightarrow\:\frac{{dx}}{{dt}}=\mathrm{3}−\mathrm{2}{y} \\…

Question-145960

Question Number 145960 by puissant last updated on 10/Jul/21 Answered by mathmax by abdo last updated on 10/Jul/21 $$\mathrm{R}_{\mathrm{n}} =\sum_{\mathrm{p}=\mathrm{n}+\mathrm{1}} ^{\mathrm{2n}} \mathrm{sin}\left(\frac{\mathrm{1}}{\mathrm{p}}\right)\:\Rightarrow\mathrm{R}_{\mathrm{n}} =_{\mathrm{p}−\mathrm{n}=\mathrm{k}} \:\:\sum_{\mathrm{k}=\mathrm{1}} ^{\mathrm{n}}…

prove-1-2-3-1-12-

Question Number 145809 by puissant last updated on 08/Jul/21 $$\mathrm{prove}\:\mathrm{1}+\mathrm{2}+\mathrm{3}+…..=−\frac{\mathrm{1}}{\mathrm{12}} \\ $$ Answered by Olaf_Thorendsen last updated on 09/Jul/21 $$\mathrm{A}\:=\:\mathrm{1}−\mathrm{1}+\mathrm{1}−\mathrm{1}+\mathrm{1}−… \\ $$$$\mathrm{A}\:=\:\mathrm{1}−\left(\mathrm{1}−\mathrm{1}+\mathrm{1}−\mathrm{1}+\mathrm{1}−…\right) \\ $$$$\mathrm{A}\:=\:\mathrm{1}−\mathrm{A} \\…