Question

change.in a+ib ( 1/1-2i + 3/1+i )( 3+4i/2-4i)​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

$\tt Let's \: z = \bigg( \frac{1}{1 - 2i} + \frac{3}{1 + i} \bigg)\bigg( \frac{3 + 4i}{2 - 4i}\bigg) \\ \\ \tt \implies\bigg( \frac{(1 + i) + 3(1 - 2i)}{(1 - 2i)(1 + i)} \bigg)\bigg( \frac{3 + 4i}{2 - 4i} \bigg) \\ \\ \tt \implies\bigg( \frac{1 + i + 3 - 6i}{1 + i - 2i - {2i}^{2} }\bigg)\bigg( \frac{3 + 4i}{2 - 4i} \bigg) \\ \\ \tt \implies \frac{1 + i + 3 - 6i}{(1 + 2) + i( - 2 + 1)} \times \frac{3 + 4i}{2 - 4i}\\ \\ \tt \implies \frac{4 - 5i}{3 -i} \times \frac{3 + 4i}{2 - 4i} \\ \\ \tt \implies \frac{12 + 16i - 15i - 20 {i}^{2} }{6 - 12i - 2i + 4 {i}^{2} }$

$\tt \implies \frac{12 + 20 + i}{6 - 4 - 14i} \\ \\ \tt \implies \frac{32 + i}{2 - 14i} \\ \\ \tt \implies \frac{32 + i}{2 - 14i} \times \frac{2 + 14i}{2 + 14i} \\ \\ \tt \implies \frac{64 + 448i + 2i + 14 {i}^{2} }{4 - 196 {i}^{2} } \\ \\ \tt \implies \frac{64 - 14 + 450i}{4 + 196} \\ \\ \tt \implies \frac{50 + 450i}{200} \\ \\ \large \boxed{\tt \green{\frac{1}{4} + \frac{9}{4}i}}$