we are given
[tex](3-7i)(p+qi)i=58i[/tex]
firstly, we will simplify left side
and then we can compare it with right side
so, we can distribute
[tex](3p+3qi-7pi-7qi^2)i=58i[/tex]
[tex](3p+3qi-7pi+7q)i=58i[/tex]
we have i on both sides
so,i will get cancelled
[tex](3p+3qi-7pi+7q)=58[/tex]
[tex](3p+7q+(3q-7p)i)=58[/tex]
we can also write as
[tex](3p+7q)+(3q-7p)i=58+0*i[/tex]
now, we can compare
and we get
[tex]3p+7q=58[/tex]
[tex]3q-7p=0[/tex]
now, we can solve for p and q
we get
[tex]q=7,\:p=3[/tex].............Answer
