What is the conjugate of (√5+12 i+√5-12i/√5+12i-√5-12i) ?

Question

What is the conjugate of (√5+12 i+√5-12i/√5+12i-√5-12i) ? (A) -3i (B) 3i (C) (3/2)i (D) -(3/2)i

Tardigrade Admin · Accepted Answer

Let z=(√5+12i+√5-12i/√5+12i-√5-12i)×(√5+12i+√5-12i/√5+12i+√5-12i) =(5+12i+5-12i+2√25+144/5+12i-5+12i) =(3/2i)=(3i/-2)=0-(3/2)i Therefore, the conjugate of z=0+(3/2)i

Q. What is the conjugate of $\frac{5 + 12 i + 5 - 12 i}{5 + 12 i - 5 - 12 i}$ ?

$- 3 i$

$3 i$

$\frac{3}{2} i$

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

Let $z = \frac{5 + 12 i + 5 - 12 i}{5 + 12 i - 5 - 12 i} \times \frac{5 + 12 i + 5 - 12 i}{5 + 12 i + 5 - 12 i}$
$= \frac{5 + 12 i + 5 - 12 i + 2 25 + 144}{5 + 12 i - 5 + 12 i}$
$= \frac{3}{2 i} = \frac{3 i}{- 2} = 0 - \frac{3}{2} i$
Therefore, the conjugate of $z = 0 + \frac{3}{2} i$

Q. What is the conjugate of 5+12i​−5−12i​5+12i​+5−12i​​ ?

−3i

3i

23​i

−23​i