Question

4i/2-5i

Answer 1

if \(z\) and \(w\) are complex numbers then
\[\large \frac{z}{w}=\frac{z\overline{w}}{w\overline{w}} \]
where \(\overline{z}=a-ib\) when \(z=a+ib\)

Answer 2

Rationalise it.

Answer 3

\[4i/2-5i~~~~~~->~~~~~~~4i/2-10i/2~~~~~~~->~~~~~~-6i/2~~~~~->~~~~~-3i\]

Answer 4

\[\frac{ 4\iota }{2-5\iota }\times \frac{ 2+5\iota }{2+5\iota }=\frac{ 8\iota+20\iota ^{2} }{ 4-25\iota ^{2} }\]
\[=\frac{ 8\iota-20 }{29 }\]