Question

2+3i÷3-4i =a+ib find the values of a and b​

Answer 1

Answer:

Step-by-step explanation:

\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}  

=  \frac{2}{25} + \frac{11}{25}i


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|