Willis Schultz
01/04/2023 · High School
\( \begin{array}{ccccc}\text { (i) } 2 i z_{2} & \text { (ii) } i z_{1}-i z_{2} & \text { (iii) } \frac{i}{z_{1}} & \text { (iv) } \frac{z_{2}}{i} \\ \text { If } z_{1}=3+4 i & \text { and } z_{2}=12-5 i \text {, show that } & z_{1} \cdot \bar{z}_{2}+\bar{z}_{1} \cdot z_{2} & \text { is a real number }\end{array} \)
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The expression \( z_{1} \cdot \bar{z}_{2} + \bar{z}_{1} \cdot z_{2} \) simplifies to 32, a real number.
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