Question

home > p6 precalculus 25 - 26 > assessment
assignment 3.1: complex numbers
score: 11/12 answered: 11/12
question 12
simplify:
\\(\frac{4i}{5 - 4i}\\)

Explanation:

Step1: Multiply by conjugate

Multiply numerator and denominator by $5 + 4i$.
$\frac{4i}{5 - 4i}\times\frac{5 + 4i}{5 + 4i}$

Step2: Expand numerator

Use distributive property.
$4i\times(5 + 4i)=20i+16i^{2}$
Since $i^{2}=-1$, it becomes $20i - 16=-16 + 20i$

Step3: Expand denominator

Use $(a - b)(a + b)=a^{2}-b^{2}$.
$(5 - 4i)(5 + 4i)=5^{2}-(4i)^{2}=25-16i^{2}=25 + 16=41$

Step4: Write in standard form

$\frac{-16 + 20i}{41}=-\frac{16}{41}+\frac{20}{41}i$

Answer:

$-\frac{16}{41}+\frac{20}{41}i$