Question

write this in a + bi form: 4/3i +2/5i

Answer 1

what would be the LCD?

Answer 2

15i right?

Answer 3

yeap

thus one sec

Answer 4

sure cx

Answer 5

\(\bf \cfrac{4}{3i}+\cfrac{2}{5i}\implies \cfrac{(4\cdot 5)+(3\cdot 2)}{15i}\implies \cfrac{(20)+(6)}{15i}\implies \cfrac{26}{15i}
\\ \quad \\
\textit{now, to rationalize it, we multiply top and bottom by }i
\\ \quad \\
\cfrac{26}{15i}\cdot \cfrac{i}{i}\implies \cfrac{26i}{15i^2}\qquad {\color{brown}{ i^2=-1}}\qquad \cfrac{26i}{15({\color{brown}{ -1}})}\implies \cfrac{26i}{-15}\implies ?\)

Answer 6

dont you multiply -i?

Answer 7

nope.... -i?
to "rationalizate", we would want to get rid of the "i" in the denominator
so we use "i" to get \(i^2\)

Answer 8

\(\bf \cfrac{26}{15i}\cdot \cfrac{i}{i}\implies \cfrac{26i}{15i^2}\qquad {\color{brown}{ i^2=-1}}\qquad \cfrac{26i}{15({\color{brown}{ -1}})}\implies \cfrac{26i}{-15}
\\ \quad \\
-\cfrac{26i}{15}\implies
\begin{cases}
a&+bi\\
\bf 0&-\cfrac{26}{15}i
\end{cases}\)

Answer 9

oh ok thnx cx