# How do you write the following quotient in standard form (6-7i)/i?

Oct 6, 2016

I found: $- 7 - 6 i$
You need to get rid of the $i$ at the denominator first. To do that you can multiply and divide by the complex conjugate of the denominator;
given a complex number in the form $a + i b$ the complex conjugate will be $a - i b$ (change the sigh of the imaginary part). In your case you have $0 + i$ and the complex conjugate will be $0 - i$.
$\frac{6 - 7 i}{0 + i} \cdot \frac{0 - i}{0 - i} =$
multiplying and remembering that ${i}^{2} = - 1$ we get:
$\frac{- 6 i + 7 {i}^{2}}{- {i}^{2}} = \frac{- 7 - 6 i}{1} = - 7 - 6 i$ in standard form.