Question

write in the form a+ib (1+3i)(1-2i)/(2+i)(4+2i)

Answer 1

Step-by-step explanation:

We have,

$\frac{(1 + 3i)(1 - 2i)}{2(2 + i)(2 + i)} = \frac{7 + i}{2(3 + 4i)}$

$= \frac{(7 + i)(3 - 4i)}{2(9 + 16)}$

$= \frac{17 - 25i}{50}$

$= \frac{17}{50} - \frac{1}{2} i$

Answer 2

Step-by-step explanation:

$\frac{(1 + 3i)(1 - 2i)}{(2 + i)(4 + 2i)} \\ \\ = \frac{1 - 2i + 3i + 6}{8 + 4i + 4i - 2} \\ \\ = \frac{7 + i}{6 + 8i} \\ \\ = \frac{7 + i}{6 + 8i} \times \frac{6 - 8i}{6 - 8i} \\ \\ = \frac{42 - 56i + 6i + 8}{36 + 64} \\ \\ = \frac{50 - 50i}{100} \\ \\ = \frac{1 - i}{2} \\ \\ = \frac{1}{2} - i \frac{1}{2}$