Question Identify a necessary and sufficient condition for two complex numbers a, b to have a real sum and a real product

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 #SPJ4 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. Reply

real numbers.What arecomplex numbers?Complex numbersare made up of two parts: a real number and an imaginary number.algebra.imaginary partmust be zero, hence bc+ad=0 or:real numbers.complex numbershere:https://brainly.com/question/16835201The correct question is given below: