Question

Given that i² = − 1, simplify
1-i (over)
-3-5i

Answer 1

`\Large \textsf{Read below}`

Explanation:

`\Large \text{$ \sf (1 - i)/(-3-5i) = \left((1 - i)/(-3-5i)\right).\left((-3 + 5i)/(-3+5i)\right)$}`

`\Large \text{$ \sf (1 - i)/(-3-5i) = (-3 + 5i + 3i -5i^2)/(9 - 15i + 15i -25i^2)$}`

`\Large \text{$ \sf i^2 = -1$}`

`\Large \text{$ \sf (1 - i)/(-3-5i) = (-3 + 5i + 3i -5(-1))/(9 - 15i + 15i -25(-1))$}`

`\Large \text{$ \sf (1 - i)/(-3-5i) = (-3 + 5i + 3i +5)/(9 - 15i + 15i +25)$}`

`\Large \text{$ \sf (1 - i)/(-3-5i) = (2 + 8i)/(34)$}`

`\Large \boxed{\boxed{\text{$ \sf (1 - i)/(-3-5i) = (1)/(17) + (4)/(17)\:i$}}}`