Question 4, Exercise 1.2

Solutions of Question 4 of Exercise 1.2 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.

If $z_{1}=2-3 i$ and $\left|z_{1} z_{2}\right|=16$ find $\left|z_{2}\right|$.

Solution.

Given $$z_{1}=2-3i$$ Then $$\begin{align}|z_1|&=\sqrt{(2)^2+(-3)^2}\\ &=\sqrt{13}\end{align}$$ Now \begin{align}&|z_{1} z_{2}|=16\\ \Rightarrow \quad &|z_{1}|| z_{2}|=16\\ \Rightarrow \quad & \sqrt{13}|z_2|=16\\ \Rightarrow \quad & |z_2|=\dfrac{16}{\sqrt{13}}\end{align}

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