+0

# Complex numbers

0
95
2

Simplify (1 - i)/(2 + 3i - 4 + 5i), where i^2 = -1.

Jul 27, 2022

#1
+2448
0

Combine like terms: $${1 - i \over 8i -2}$$

Multiply by $${8i + 2 \over 8i + 2}$$$${(1 -i)(8i + 2) \over {(8i - 2)(8i + 2)}}$$

Expand: $${-8i^2 + 6i + 2 \over 64i^2 - 4}$$

Substitute $$i^2 = -1$$$${8 + 6i + 2 \over -64 - 4}$$

Combine like terms: $${10 + 6i \over -68}$$

Simplify: $$\color{brown}\boxed{- 5 - 3i \over 34}$$

Jul 27, 2022
#2
+51
+2

BuilderBoi, your answer is correct, however I'm pretty sure to express that answer as a complex number you would write it as

$$\frac{-5}{34}-\frac{3}{34}i$$

Jul 28, 2022