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Question

The conjugate of the complex number $$\displaystyle \frac {2 + 5}{4 - 3i} $$is


A
726i25
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B
726i25
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C
7+26i25
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D
7+26i25
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Solution

The correct option is C $$\displaystyle \frac{-7 + 26i}{25}$$
Conjugate of $$\dfrac{2+5i}{4-3i}$$

$$=\dfrac { \left( 2+5i \right) \left( 4+3i \right)  }{ \left( 4-3i \right) \left( 4+3i \right)  } $$

$$=\dfrac { 8+6i+20i-15 }{ { \left( 4 \right)  }^{ 2 }-{ \left( 3i \right)  }^{ 2 } } $$

$$=\dfrac { -7+26i }{ 25 } $$

Hence, the answer is $$\dfrac { -7+26i }{ 25 }.$$

Mathematics

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