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

Question

asked Sep 1, 2020 46.0k views

2 Answers

Kiril Mytsykov · Answer 1 · 2020-09-08T08:38:16+0000

Answer:

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

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:

$i=√(-1)\\\\i^2 = -1$

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