Question

More help I need lots of help mostly mentally but this too

Answer 1

C

Step-by-step explanation:

You could solve this problem just by plugging in all the answers until you got a real number, but a more elegant solution is to look to see which value of y will cancel out the first instance of i.

Since the first instance is 5i, -5i should cancel it out. We can see that C had -5 as it's y value, so we know that it's correct.

To verify, run it through your calculator:

`(4 + 5i)(4 + - 5i) = 41`

Since 41 is a real number, we know it's correct.

Hope this helps!

p.s. here's some mental help too *sends loves hugs and coffee* <3

Answer 2

Answer: C) x = 4 and y = -5

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Step-by-step explanation:

If we multiply some complex number a+bi with its conjugate a-bi, then we get the real number a^2+b^2. You can use the FOIL rule to confirm that (a+bi)(a-bi) = a^2+b^2 is true. Recall that i = sqrt(-1), so i^2 = -1.

In this case, a = 4 and b = 5, so,

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

(4+5i)(4-5i) = 4^2+5^2

(4+5i)(4-5i) = 41

We see that x = 4 and y = -5 must be the case.