Home › AP EAMCET › Mathematics › Complex Numbers and Quadratic Equations › What is the real part of the reciprocal of a + i…
What is the real part of the reciprocal of a + ib (not both zero)?
Aa/(a² + b²)
Ba/(a² − b²)
C−b/(a² + b²)
Da²/(a² + b²)
Answer & Solution
Correct answer: A. a/(a² + b²)
1/(a + ib) = (a − ib)/(a² + b²), whose real part is a/(a² + b²).
Related questions
If x is real and |x + 3i| = 5, which values can x take?Which property explains why (2 + 3i)(1 − i) equals (1 − i)(2 + 3i)?Because complex numbers obey the usual associative, commutative and distributive laws, whaIf z = −z̄ for a complex number z, which statement is correct?If a complex number z equals its own conjugate, what kind of number is z?For z = a + ib, the sum z + z̄ equals what?Taking the conjugate of the conjugate of z gives which result?What is the conjugate of the product (2 + i)(3 − i)?