ข้อสอบคณิต 9 สามัญ - ปี 2560

สมมติให้ z = a + bi และ $\overline{\mathrm{z}}$ = a - bi

$$\begin{gathered} \mathrm{จากโจทย์} z+\left|\frac{\overline{z}-1}{z-1}\right| = -3+2\mathrm{i} \\ \mathrm{จะได้} (\mathrm{a}+\mathrm{bi})+\left|\frac{(\mathrm{a}-\mathrm{bi}) -1}{(\mathrm{a}+\mathrm{bi})-1}\right|=-3+2\mathrm{i} \\ (\mathrm{a}+\mathrm{bi})+\frac{\sqrt{{(\mathrm{a}-1)}^2+{(-\mathrm{b})}^2}}{\sqrt{{(\mathrm{a}-1)}^2+{\left(\mathrm{b}\right)}^2}}=-3+2\mathrm{i} \\ (\mathrm{a}+\mathrm{bi}) +1 = -3+2\mathrm{i} \\ \mathrm{a}+\mathrm{bi} = -4+2\mathrm{i} \\ \mathrm{ดังนั้น} z = -4+2\mathrm{i} \end{gathered}$$

$$\begin{gathered} \mathrm{ดังนั้น} \left|z\right| = \sqrt{{\left(-4\right)}^2+2^2} \\ = \sqrt{20} \\ = 2\sqrt{5} \end{gathered}$$