Question

Simplify the expression the root of negative 1 all over the quantity of 2 minus 4 i minus the quantity of 5 plus 3 i.

Answer 1

Do yo mean: \[\frac{ i }{ 2-4i-(5+3i) }\]

Answer 2

@ZeHanz yes exactly what i mean

Answer 3

Then the first step is to calculate the difference in the denominator:\[\frac{ i }{ (2-5) -(4+3)i }=\frac{ i }{ -3-7i }\]Next is a standard trick to get rid of the complex number in the denominator: multiply nominator and denominator with -3+7i (the conjugate of -3-7i):\[\frac{ i }{ -3-7i }\frac{ -3+7i }{ -3+7i }=\]
Because you know what happens when you write out (a-b)(a+b), can you do the rest yourself now?

Answer 4

so @ZeHanz whats the answer?

Answer 5

@ZeHanz ???

Answer 6

\[\frac{ i(-3+7i) }{ 9+49 }=\frac{ -7-3i }{ 58 }\]