Question

express the complex number 2+i/3-4i in the form a+ib and find its modulus .
Plz help me

Answer 1

$\frac{2+i}{3-4i}$

= $\frac{2+i}{3-4i}$ × $\frac{3+4i}{3+4i}$ = $\frac{6+8i+3i-4}{9-(-16)}$ = $\frac{2+11i}{25}$

= [tex] \frac{2}{25} + \frac{11}{25}i [/tex]

Finding modulus:
|Z| = $\sqrt{a^2+b^2}$

= $\sqrt{( \frac{2}{25} )^2+( \frac{11}{25})^2 }$
= $\sqrt{ \frac{4}{625} +\frac{121}{625} }$
= $\sqrt{ \frac{125}{625} }$
= $\frac{5 \sqrt{5} }{25}$
= $\frac{ \sqrt{5} }{5}$
= $\frac{1}{ \sqrt{5} }$ = |Z|