Answer:
= [tex]\frac{5}{29} +\frac{2i}{29}[/tex] is True
Step-by-step explanation:
[tex]\frac{1}{5-2i }[/tex]
=[tex]\frac{1}{5-2i }[/tex]×[tex]\frac{5+2i }{5+2i }[/tex] ∴ Multiply and divide with conjugate of 5-2i.
=[tex]\frac{5+2i }{(5-2i )(5+2i )}[/tex]
=[tex]\frac{5+2i }{(5^{2} )-(2i^{2} )}[/tex]
=[tex]\frac{5+2i }{(5^{2} )-(2i^{2} )}[/tex]
=[tex]\frac{5+2i }{( 25 )-(-4 )}[/tex]
=[tex]\frac{5+2i }{25 +4 }[/tex]
=[tex]\frac{5+2i }{29 }[/tex]
=[tex]\frac{5}{29} +\frac{2i}{29}[/tex]
