Answer:
[tex](2-5i)(p+q)(i)=29i[/tex]
Step-by-step explanation:
We have the product of 2 complex numbers
[tex](2-5i)(p+q)(i)[/tex]
We know that:
[tex]p=2\\\\q=5i[/tex]
Then we substitute these values in the expression
[tex](2-5i)((2)+(5i))(i)[/tex]
[tex](2-5i)(2+5i)(i)[/tex]
The product of a complex number [tex]a + bi[/tex] by its conjugate [tex]a-bi[/tex] is always equal to:
[tex]a ^ 2 - (bi) ^ 2[/tex]
Then
[tex](2-5i)(2+5i)(i)=(2^2-5^2i^2)(i)[/tex]
Remember that:
[tex]i=\sqrt{-1}\\\\i^2 = -1[/tex]
So
[tex](2^2-5^2i^2)(i)= (4 - 25(-1))(i)\\\\(4 - 25(-1))(i) = (4+25)i=29i[/tex]
Finally
[tex](2-5i)(p+q)(i)=29i[/tex]
