Question

Which values of p and q would make the value of the following expression equal to 29i? (2 – 5i)(p + q)i A.p = 2, q = 5i B.p = –2, q = 5i C.p = 2, q = –5i D.p = –2, q = –5i

Answer 1

`(2-5i)(p+q)i=29i \ \ \ \ \ \ \ \ |/ i \\ (2-5i)(p+q)=29 \ \ \ \ \ \ \ \ \ \ |/ (2-5i) \\ p+q=(29)/(2-5i) \\ \\ \overline{\underline{(29)/(2-5i)=(29(2+5i))/((2-5i)(2+5i))=(29(2+5i))/(2^2-(5i)^2)=(29(2+5i))/(4-25i^2)=(29(2+5i))/(4+25)=(29(2+5i))/(29)=2+5i}} \\ \\ p+q=2+5i`

In your answer options p is a real number and q is an imaginary number, so p=2 and q=5i.

The answer is A.