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

expand first:
(2 – 5i)(p + q)i =

Answer 2

Okay @SolomonZelman could probably explain exactly how to do this because he is smart like that but I was able to pass the SAT by plugging these things in so lets start with A.

Answer 3

(2-5i)(2+5i)i
4 - 10i + 10i - 25i^2
4 - 10i + 10i - 25(-1)
4 - 0i - (-25)
4 + 25
29

Answer 4

@SolomonZelman just check my problem on A so I know I am not giving @dreamstoogood wrong info.

Answer 5

u need it to equal 29i, not 29

Answer 6

o.o What did I do wrong?

Answer 7

(2 – 5i)(p + q)i=29i

(in a+bi form, it is 0+29i)

(2 – 5i)(p + q)i = expands to >> 2p+2q-5pi-5qi

so,

2p+2q-5pi-5qi=29i

in a+bi form,

(2p+2q)+(-5p-5q)i=0+29i

therefore

2p+2q=0
(-5p-5q)i=29i

Answer 8

so there is a system of equations to solve

Answer 9

you can cancel i' in equation 2, and from that point and on it is just algebra.