Questions: Evaluate the expression (-4-1 i)/(8 i) and write the result in the form a+bi. The real number a equals The real number b equals

Transcript text: Evaluate the expression $\frac{-4-1 i}{8 i}$ and write the result in the form $a+b i$. The real number $a$ equals $\square$ The real number $b$ equals $\square$

Solution

Solution Steps

Step 1: Identify the operation

The operation to perform is division.

Step 2: Apply the formula for division

Given two complex numbers $a+bi$ and $c+di$, their quotient is $ rac{(ac+bd) + (bc-ad)i}{c^2+d^2}$.

Step 3: Perform the calculation

Since division involves the conjugate, we first find the conjugate of the denominator and then perform the operation. After performing the division, the result is $ -0.12 + 0.5i $.