Question

Find the conjugate of 2 - 5i and then calculate the product of the given complex

number and its conjugate. (1 point)
O The conjugate is –2 + 5i and the product is -4 - 201 - 2522.
The conjugate is 2 + 5i and the product is 4 -
2522
O The conjugate is -2 + 5i and the product is - 29.
The conjugate is 2 + 5i and the product is 29.
JUST ONE MORE !! PLS

Answer 1

Okay yes but t is 29 and I hopes this helps good luck

Answer 2

The conjugate is 2+5i and the product is 29.

Explanation:

The conjugate of a complex number
`a+bi` is
`a-bi`

Our complex number is 2-5i.

Here, a = 2 and b = -5

Thus, the conjugate of 2-5i is

`2-(-5i)=2+5i`

Using this rule:

`(a+b)(a-b)=a^(2)-b^(2)`

And the fact that
`i^(2) = -1`

We can find the product of any complex number and its conjugate:

`(a+bi)(a-bi)=a^(2) - (bi)^(2)=a^(2) - b^(2) i^(2) = a^(2) + b^(2)`

As our complex number is
`2-5i`, the product with its conjugate will be

`2^(2) + (-5)^(2) =4+25=29`