Answers

1. Either both numbers are conjugated or both numbers are real numbers.

   What are complex numbers?

   • Complex numbers are made up of two parts: a real number and an imaginary number.
   • Complex numbers serve as the foundation for more complex math, such as algebra.

   Consider two complex numbers q and p such that,q=c+id and p=a+ib.

   • A.T.Q. PQ is real and p + q real.
   • pq=(ac−bd)+(bc+ad)i

   Since PQ is real, the imaginary part must be zero, hence bc+ad=0 or:

   • bc=−ad

   Then,

   • p+q=(a+c)+(b+d)i

   Here also b+d must be zero or:

   • d=−b

   So putting d=−b in bc=−ad, we will get,

   • b(c−a)=0

   So either,

   • b=d=0
   • or, a=c,b=−d

   So either p and q are conjugated

   • p=a+bi,q=a−bi

   or both are real

   • p=a,q=c

   Therefore, either both numbers are conjugated or both numbers are real numbers.

   Know more about complex numbers here:

   https://brainly.com/question/16835201

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   The correct question is given below:

   If the product and the sum of two complex numbers are real, what can we say about the numbers? Prove it.

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