Question

write in standard form
Z=-2-5i/3-6i​

Answer 1

$\frac{4}{5} - \frac{1}{15} i$

Step-by-step explanation:

$Given, \: \: z= \frac{2 - 5i}{3 - 6i} \\ = \frac{2 - 5i}{3 - 6i} \times \frac{3 + 6i}{3 + 6i} \\ = \frac{(2 - 5i)(3 + 6i)}{(3)^{2} - (6i)^{2} } \\ = \frac{2 \times 3 + 2 \times 6i - 5i \times 3 - 5i \times 6i}{9 - 36 {i}^{2} } \\ = \frac{6 + 12i - 15i - 30 {i}^{2} }{9 - 36 {i}^{2} } \\ we \: \: know \: \: that \: \: \boxed{i = \sqrt{ - 1} \: = > \: {i}^{2} = - 1 } \\ Now, \: \: putting \: \: value \\ = \frac{6 - 3i - 30 \times (- 1)}{9 - 36 \times ( - 1)} \\ = \frac{6 - 3i + 30}{9 + 36} \\ = \frac{36 - 3i}{45} \\ = \frac{36}{45} - \frac{3}{45}i \\ = \boxed{ \frac{4}{5} - \frac{1}{15} i}$