Question

Complex numbers help. *question attached below* Will give medal.

Answer 1

So I got this question in an exam the other day, and was clueless as to what to do. Can someone help me with it please so that I will understand what to do incase it comes again ?

Answer 2

Ok - you are given:\[(1+5i)p-2q=3+7i\]and the first question is: "if p and q are real what are their values?"

Use the fact that two complex numbers are equal if their real components equal one another and also their imaginary components equal one another.

i.e. if:\[a+ib=c+id\]then this means that:\[a=c\]and:\[b=d\]

Answer 3

so first rearrange the left-hand-side in the form: \(a+ib\)

Answer 4

Would we have to simplify (1+5i)p?

Answer 5

separate the "real" and "imaginary" compnents

Answer 6

Real - 1
Imaginary - 5

Answer 7

almost...\[(1+5i)p-2q=p+5pi-2q=(p-2q)+(5p)i\]this is now in the form \(a+bi\)

Answer 8

Yes

Answer 9

Now you can compare real and imaginary components and solve the resulting equations