Question 5, Review Exercise

Solutions of Question 5 of Review Exercise of Unit 01: Complex Numbers. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan.

Find $z$ when $(z-3 i)(2+5 i)=3-4 i$.

Solution.

Find $z$ when $(z-3 i)(2+5 i)=3-4 i$.

Solution.

\begin{align*} &(z-3 i)(2+5 i)=3-4 i \\ \implies & z-3 i=\dfrac{3-4 i}{2+5 i} \\ \implies & z-3 i=\dfrac{(3-4 i)(2-5i)}{(2+5 i)(2-5i)}\\ \implies & z-3 i=\dfrac{6-20-15i-8i}{4+25}\\ \implies & z-3 i=\dfrac{-14-23i}{29}\\ \implies & z=-\dfrac{14}{29}-\dfrac{23i}{29}+3i\\ \implies & z=-\dfrac{14}{29}+\dfrac{64i}{29}.\\ \end{align*}

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