Question

Find the conjugate of the complex number 5-7i/5+8i

Answer 1

Answer:

To find a complex conjugate, simply change the sign of the imaginary part (the part with the i ). This means that it either goes from positive to negative or from negative to positive. ... Therefore, the complex conjugate of 5−7i is 5+7i.

Answer 2

Answer:

$\tt{\dfrac{-31}{89}+\dfrac{75}{89}i}$

Step-by-step explanation:

$\sf{\dfrac{5-7i}{5+8i}}$

Multiply by (5 - 8i) in both numerator and denominator.

$\dashrightarrow \: \: \sf{\dfrac{5-7i}{5+8i}\times\dfrac{5-8i}{5-8i}}$

$\dashrightarrow \: \: \sf{\dfrac{5(5-8i)-7i(5-8i)}{5^{2}-(8i)^{2}}}$

$\dashrightarrow \: \: \sf{\dfrac{25-40i-35i+56i^{2}}{25-64i^{2}}}$

We know that i² = -1.

$\dashrightarrow \: \: \sf{\dfrac{25-75i-56}{25+64}}$

$\dashrightarrow \: \: \sf{\dfrac{-31-75i}{89}}$

$\dashrightarrow \: \: \sf{\dfrac{-31}{89}-\dfrac{75}{89}i}$

So its conjugate will be:

$\hookrightarrow \: \: \boxed{\bf{\dfrac{-31}{89}+\dfrac{75}{89}i}}$