Math, asked by GauravBorase, 10 months ago

show that 1-2i/3-4i+1+2i/3+4i is real​

Answers

Answered by bedabrata85
33

SOLUTION

Mate here is your Solution please mark braineliest

 \frac{1 - 2i}{3 - 4i}  +  \frac{1 + 2i}{3 + 4i}  \\  =  \frac{(1 - 2i)(3 + 4i) + (1 + 2i)(3 - 4i)}{ {3}^{2}  -  {(4i)}^{2} }  \\  =  \frac{3 + 4i - 6i - 8 {i}^{2}  + 3 - 4i + 6i - 8 {i}^{2} }{9 - 4 \times ( - 1) }   \\  =  \frac{6 - 16 \times ( - 1) }{9 + 4}   \\  =  \frac{22}{13}

Therefore , the given expression is real

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