Write (1/3i)-(-6+2/3i) as a complex number in standard form
Accepted Solution
A:
Answer:[tex]6+\frac{i}{3}[/tex]Step-by-step explanation:[tex]\frac{1}{3\imath}-(-6+\frac{2}{3\imath})[/tex][tex]\frac{1}{3\imath}+6-\frac{2}{3\imath}[/tex]taking like terms together[tex]\frac{1}{3\imath}-\frac{2}{3\imath}+6[/tex]taking LCM[tex]\frac{1-2}{3\imath}+6[/tex][tex]\frac{-1}{3\imath}+6[/tex]taking LCM[tex]\frac{-1+18\imath}{3\imath}[/tex]splitting the term [tex]\frac{-1+18\imath}{3\imath}[/tex]splitting the term [tex]-\frac{1}{3\imath}+\frac{18\imath}{3\imath}[/tex][tex]-\frac{1\times3\imath}{3\imath \times \imath}+6[/tex][tex]-\frac{i}{3\imath^2}+6[/tex]we know that [tex]\imath^2=-1[/tex]putting this value in above equation [tex]\frac{\imath}{3}+6[/tex]