Questions: Divide. -6/(1-4 i) Write your answer as a complex number

Transcript text: Divide. \[ \frac{-6}{1-4 i} \] Write your answer as a complex numbe

Solution

Solution Steps

Step 1: Multiply by the complex conjugate of the denominator

To divide two complex numbers, we multiply the numerator and the denominator by the complex conjugate of the denominator.

Step 2: Apply the multiplication

The multiplication is applied as follows: $$\frac{a + bi}{c + di} \cdot \frac{c - di}{c - di} = \frac{(a + bi)(c - di)}{c^2 + d^2}$$

Step 3: Expand the numerator and simplify the expression

After expanding and simplifying, we get: $$\frac{ac + bd + (bc - ad)i}{c^2 + d^2}$$ Which simplifies to: $$a = \frac{-6\cdot1 + 0\cdot-4}{1^2 - 4^2}, \quad b = \frac{0\cdot1 + 6\cdot-4}{1^2 - 4^2}$$

Final Answer:

The result of dividing the complex numbers is -0.35 - 1.41i

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