Reciprocal

Calculate reciprocal of z=0.8-1.8i:

Correct answer:

Re =  0.21
Im =  0.46

Step-by-step explanation:

$$\begin{gathered} {\displaystyle \frac{1}{z}}={\displaystyle \frac{1}{0.8-1.8i}}={\displaystyle \frac{1}{0.8-1.8i}}\mathrm{.}{\displaystyle \frac{0.8+1.8i}{0.8+1.8i}} \\ Re{\displaystyle \frac{1}{z}}={\displaystyle \frac{0.8}{0.8^2+(-1.8{)}^2}}=0.21 \end{gathered}$$

$$\begin{gathered} Im{\displaystyle \frac{1}{z}}=-{\displaystyle \frac{-1.8}{0.8^2+(-1.8{)}^2}}=0.46 \\ {\displaystyle \frac{1}{z}}=0.21+0.46i \end{gathered}$$

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