Divide. Express your answer in standard form. $$ \frac{-4 i}{1+i} $$

Question

UpStudy AI · Accepted Answer

To divide the complex numbers $$\frac{-4i}{1+i}$$ and express the result in standard form $$a + bi$$, follow these steps:

1. **Multiply the numerator and the denominator by the conjugate of the denominator:**

The conjugate of $$1 + i$$ is $$1 - i$$.

$$
   \frac{-4i}{1+i} \times \frac{1-i}{1-i} = \frac{-4i(1-i)}{(1+i)(1-i)}
   $$

2. **Simplify the denominator:**

$$
   (1+i)(1-i) = 1^2 - i^2 = 1 - (-1) = 2
   $$

3. **Expand the numerator:**

$$
   -4i(1-i) = -4i + 4i^2 = -4i + 4(-1) = -4i - 4
   $$

4. **Combine the results:**

$$
   \frac{-4i - 4}{2} = \frac{-4}{2} + \frac{-4i}{2} = -2 - 2i
   $$

**Final Answer:**
$$-2 - 2i$$
$$-2 - 2i$$

Divide. Express your answer in standard form. \( \frac{-4 i}{1+i} \)