Question

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

Answer 1

Answer:

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

Step-by-step 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

$2^{2} + (-5)^{2} =4+25=29$

Answer 2

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