Question

Evaluate (2-5i)(p+q)(i) when p=2 and q=5i.

Answer 1

Answer:

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

Step-by-step explanation:

We have the product of 2 complex numbers

$(2-5i)(p+q)(i)$

We know that:

$p=2\\\\q=5i$

Then we substitute these values in the expression

$(2-5i)((2)+(5i))(i)$

$(2-5i)(2+5i)(i)$

The product of a complex number $a + bi$ by its conjugate $a-bi$ is always equal to:

$a ^ 2 - (bi) ^ 2$

Then

$(2-5i)(2+5i)(i)=(2^2-5^2i^2)(i)$

Remember that:

$i=\sqrt{-1}\\\\i^2 = -1$

So

$(2^2-5^2i^2)(i)= (4 - 25(-1))(i)\\\\(4 - 25(-1))(i) = (4+25)i=29i$

Finally

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