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Question-201357




Question Number 201357 by sonukgindia last updated on 05/Dec/23
Commented by mahdipoor last updated on 05/Dec/23
(1−4i)z=4ni⇒z=((4ni)/(1−4i))=((4n(4+i))/(17))  im(z)=((4n)/(17))=164⇒n=17×41=697  z=656+164i
$$\left(\mathrm{1}−\mathrm{4}{i}\right){z}=\mathrm{4}{ni}\Rightarrow{z}=\frac{\mathrm{4}{ni}}{\mathrm{1}−\mathrm{4}{i}}=\frac{\mathrm{4}{n}\left(\mathrm{4}+{i}\right)}{\mathrm{17}} \\ $$$${im}\left({z}\right)=\frac{\mathrm{4}{n}}{\mathrm{17}}=\mathrm{164}\Rightarrow{n}=\mathrm{17}×\mathrm{41}=\mathrm{697} \\ $$$${z}=\mathrm{656}+\mathrm{164}{i} \\ $$

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