TS EAMCET · Maths · Complex Number
One of the values of \(\sqrt{24-70 i}+\sqrt{-24+70 i}\) is
- A \(2+12 i\)
- B \(12-2 i\)
- C \(-12+2 i\)
- D \(-12-2 i\)
Answer & Solution
Correct Answer
(D) \(-12-2 i\)
Step-by-step Solution
Detailed explanation
\(\sqrt{24-70 i} = a+bi\) \(a^2-b^2=24, \quad 2ab=-70, \quad a^2+b^2=\sqrt{24^2+(-70)^2}=74\) \(2a^2=98 \Rightarrow a=\pm 7\) \(2b^2=50 \Rightarrow b=\pm 5\) \(ab=-35 \Rightarrow \sqrt{24-70 i} = \pm (7-5i)\) \(\sqrt{-24+70 i} = c+di\)…
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