Question

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

Answer 1

29i

Explanation:

Edge Verified

Answer 2

`(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`