Question

question 22
score: 0 of 1 point
divide and express the result in standard form.
$\frac{3 + 2i}{7 - 7i}=$ enter your answer
note: show your result in the form $a + bi$ and use reduced fractions where needed.
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Explanation:

Step1: Multiply by conjugate

Multiply numerator and denominator by the conjugate of the denominator $7 + 7i$.
$\frac{3 + 2i}{7-7i}\times\frac{7 + 7i}{7 + 7i}$

Step2: Expand numerator

Use FOIL method: $(3 + 2i)(7 + 7i)=3\times7+3\times7i+2i\times7+2i\times7i = 21+21i + 14i+14i^{2}$. Since $i^{2}=-1$, it becomes $21 + 35i-14=7 + 35i$.

Step3: Expand denominator

$(7 - 7i)(7 + 7i)=7^{2}-(7i)^{2}=49-49i^{2}=49 + 49=98$.

Step4: Simplify fraction

$\frac{7 + 35i}{98}=\frac{7}{98}+\frac{35i}{98}=\frac{1}{14}+\frac{5}{14}i$

Answer:

$\frac{1}{14}+\frac{5}{14}i$