Question

Write (1/3i)-(-6+2/3i) as a complex number in standard form

Answer 1

Answer:

$6+\frac{i}{3}$

Step-by-step explanation:

$\frac{1}{3\imath}-(-6+\frac{2}{3\imath})$

$\frac{1}{3\imath}+6-\frac{2}{3\imath}$

taking like terms together

$\frac{1}{3\imath}-\frac{2}{3\imath}+6$

taking LCM

$\frac{1-2}{3\imath}+6$

$\frac{-1}{3\imath}+6$

taking LCM

$\frac{-1+18\imath}{3\imath}$

splitting the term

$\frac{-1+18\imath}{3\imath}$

splitting the term

$-\frac{1}{3\imath}+\frac{18\imath}{3\imath}$

$-\frac{1\times3\imath}{3\imath \times \imath}+6$

$-\frac{i}{3\imath^2}+6$

we know that

$\imath^2=-1$

putting this value in above equation

$\frac{\imath}{3}+6$