Question

Write expression as a complex number in standard form and show work please!!!
[(13i)/(1-2i)]
The i is imaginary number. :) Thanks!

Answer 1

your job is to multiply top and bottom by the conjugate of
\[1-2i\] which is
\[1+2i\]

Answer 2

this works because it is always true that
\[(a+bi)(a-bi)=a^2+b^2\] a real number

Answer 3

\[\frac{13i}{1-2i}\times \frac{1+2i}{1+2i}=\frac{13i(1+2i)}{1^2+2^2}\]
\[\frac{13i(1+2i)}{5}\]
\[\frac{13i-23}{5}\]

Answer 4

typo on last line, should be
\[\frac{13i-26}{5}\] in standard form
\[-\frac{26}{5}+\frac{13}{5}i\]