Questions: Divide. 5+7 i / 1+i 5+7 i / 1+i (Simplify your answer. Type your answer in the form a +bi.)

Transcript text: Divide. \[ \begin{array}{l} \frac{5+7 i}{1+i} \\ \frac{5+7 i}{1+i}= \end{array} \] $\square$ (Simplify your answer. Type your answer in the form a +bi .)

Solution

Solution Steps

Step 1: Multiply by the Conjugate

To simplify the fraction $\frac{5 + 7i}{1 + i}$, we multiply both the numerator and the denominator by the conjugate of the denominator, which is $1 - i$.

Step 2: Apply the Distributive Property

After applying the distributive property, the numerator becomes $5 + 7 + (7 - 5)i$ and the denominator becomes $1 + 1$.

Step 3: Combine Like Terms

Combining like terms, we get $12 + 2.0i$ over $2$ in the denominator.

Step 4: Simplify the Fraction

Finally, dividing the real and imaginary parts of the numerator by the real number in the denominator, we get $6 + 1.0i$.