Question

5.Find the product of (x + (3+5i))^2. please help I have no idea what to do!

Answer 1

@ganeshie8

Answer 2

(a+b)^2 = a^2 + 2 ab+ b^2

in your case:

a= x
b = 3+5i


( so when you come to evaluate b^2 you need to do the same above)

I cannot reply soon - but give it a try in slow steps, based on the expansion I gave you above....

Answer 3

I have no idea if what I did is correct. I don't think it is.

Answer 4

@Kainui

Answer 5

Show us what you did, and we can help you out.

Answer 6

well I did what MrNood said and I got (x + 3 + 5i)^2 = x^2 + 2(x)(3 + 5i) + 3 + 5i^2

Answer 7

and tgen when I multiplied the 2(x)(3 + 5i), I got, 6x + 10xi

Answer 8

You might want to put add a couple parenthesis at the end, otherwise, it's perfect:

x^2 + 2(x)(3 + 5i) + (3 + 5i)^2

So now you can use the same rules you just used on this thing to just this one part: (3 + 5i)^2 and then you'll have all the terms.

Answer 9

so it's x^2 + (6x + 10xi) + (3 + 5i)^2 ? or do I have to keep going some how?

Answer 10

Yep, good job for that middle part too. =)

Answer 11

thanks :) so im done?

Answer 12

Not yet, you still have to multiply out this term: (3 + 5i)^2

Answer 13

oh so is it 3^ + 5i^2, which is 9 + 25i?

Answer 14

Nope, almost though, you're just missing the middle term, remember what @MrNood said earlier: (a+b)^2 = a^2 + 2 ab+ b^2 this time a and b are slightly different for this part.

Answer 15

I don't understand

Answer 16

Try to understand, reread and think about it for a little bit.

To help you understand (a+b)^2 = a^2 + 2 ab+ b^2 replace a and b with numbers like a=3 and b=2 and work through it.

Answer 17

so just plug random numbers into (a+b)^2 = a^2 + 2 ab+ b^2 ?

Answer 18

Really you're just distributing, for instance if I tell you to multiply 5*5 you can write 25 or we can write it like 5*(2+3) since 2+3=5 right? So distribute the 5 and you have 5*2+5*3 which is 10+15 right? That's also just 25! Now write the 5s in this formula 5*2+5*3 as (2+3) and we have (2+3)*2 + (2+3)*3 and we distribute these to get 2*2+3*2+2*3+3*3. But notice that the middle terms are the same and the other terms are square so we have 2^2+2(2*3)+3^2 But hey! That was 5*5 to begin with! So that's why the whole (2+3)(2+3)=2^2+2(2*3)+3^2 equation works out.

Answer 19

so what am I doing with the 5's? sorry im probably making you mad im just so confused

Answer 20

going back up a few post YOU posted this:

"so it's x^2 + (6x + 10xi) + (3 + 5i)^2 ? or do I have to keep going some how?"

You are most of the way there, but you look at the last term - it needs expanding:

(3 + 5i)^2 is in the same form (a+b)^2

where a=3
and b = 5i

so expand that term using (a+b)^2 = a^2 + 2 ab+ b^2

You then need to get the whole expression together again, and combine like terms as you did above.

Take it steady - it's a methodical process - you are making good progress...

Answer 21

well I was confused at first but then I just did (x + 3 + 5i)(x + 3 + 5i) and then distributed and got x^2 + 6x + 10xi – 16 + 30i

Answer 22

the term is just
(3 + 5i)^2 (there is no x in it)

You can also note that i^2 = -1

so if oyu have that in your terms you can replace it with -1