Question

(3+2i/2-5i)+(3-2i/2+5i) write in a+ib form​

Answer 1

Given expression,

$\sf{ \frac{3 + 2i}{2 - 5i} + \frac{3 - 2i}{2 + 5i} }$

To find the general form of the given expression

Now,

$\sf{ \dfrac{3 + 2i}{2 - 5i} + \frac{3 - 2i}{2 + 5i}} \\ \\ \implies \: \sf{ \dfrac{(3 + 2i)(2 + 5i) + (3 - 2i)(2 - 5i)}{(2 + 5i)(2 - 5i)} } \\ \\ \implies \: \sf{ \dfrac{(6 + 19i + 10i {}^{2} )+ (6 - 19i + 10i {}^{2}) }{2 {}^{2} - (5i ){}^{2} } } \\ \\ \implies \: \sf{\dfrac{12 +20i {}^{2} }{2 - 25i {}^{2} }} \\ \\ \sf{we \: know \: that \: i {}^{2} = - 1} \\ \\ \implies \: \sf{ \dfrac{12 - 20}{2 + 25} } \\ \\ \implies \: \sf{- \dfrac{ 8}{27} } \\ \\ \implies \: \underline{\boxed{ \sf{- \dfrac{ 8}{27} + 0i}}}$

Here,

a= -8/27 and b=0