Question

Can someone please help me quickly? I only have about 20 minutes left so can someone try and help ASAP? Here is question: Find the product of (x + (3+5i))2.

Answer 1

Find the product of (x + (3+5i))2.

Answer 2

@mathstudent55 Can you help me out here?

Answer 3

@ganeshie8 Can you help me out here?

Answer 4

Also if you can show or describe the steps that would be useful...

Answer 5

\(a(b+(c+d))=ab+a(c+d) = ab+ac+ad\)

Answer 6

let a = x and b = 3 + 5i

find \((a + b)^2 \) and then substitute back

Answer 7

@zzr0ck3r Can you elaborate? and @LarsEighner I am going to try it but what do you mean substitute back?

Answer 8

if you expanded \((a + b)^2\), replace b with 2 + 5i in the expansion.

Answer 9

@LarsEighner I got x^2+6x+40ix-16 Is that right?

Answer 10

No. I think you have add terms in ix to terms in i. I could be wrong.

Answer 11

\((x + (3+5i))^2=(x + (3+5i))(x + (3+5i))=x^2+2x(3+5i)+(3+5i)^2=\\x^2+6x+10xi+(9+30i+25i^2)=x^2+6x+10xi+9+30i-25=\\x^2+6x+10xi+30i+16\)

Answer 12

@LarsEighner what do you mean?

Answer 13

you combined \(10xi\) with \(30i\)

Answer 14

@zzr0ck3r thank you :D

Answer 15

@zzr0ck3r the square of 5i is -25

Answer 16

right, hence why I have -25

Answer 17

Something weird is going on though... Whenever I check for the answer on mathway I get that the answer is supposed to be x^2+6x+9

Answer 18

thats wrong

Answer 19

Then how come your unit term comes out +16?

Answer 20

-25+9 = 16

Answer 21

http://www.wolframalpha.com/input/?i=%28x+%2B+%283%2B5i%29%29^2

Answer 22

If it is telling you -25 + 9 = 16 it is wrong.

Answer 23

err lol -16, I wrote minus down and put + here

Answer 24

im dyslexic

Answer 25

Thank you guys! You both helped me out a lot!

Answer 26

\((x + (3+5i))^2=(x + (3+5i))(x + (3+5i))=x^2+2x(3+5i)+(3+5i)^2=\\x^2+6x+10xi+(9+30i+25i^2)=x^2+6x+10xi+9+30i-25=\\x^2+6x+10xi+30i-16\)

Answer 27

Anyway what @zzr0ck3r wrote in the big equation is right except it should by -16 at the end.

Answer 28

edit* \(\huge \ \ \ \ \uparrow\)

Answer 29

Now it is fixed

Answer 30

that much more important stuff is everything else, so I hope you understand @silca if not ask....

Answer 31

@zzr0ck3r Yeah I understand now it's just mathway was confusing me... I would get the answer you put in the first 3 trials but for some reason I got confused when I uploaded this question and wrote the wrong answer.

Answer 32

This stuff is much easier if you do not try to work it out horizonatally, but set it up like a regular multiplication.

Answer 33

\[ \large \begin{align} x +3 &+ 5i \cr x +3 &+ 5i \cr \hline 5ix + 15i &+ 25i^2 \cr 3x \quad + 9 \quad \quad \quad \quad + 15i& \cr x^2 + 3x \quad\quad \quad \quad + 5ix \quad \quad \quad & \cr\hline x^2 + 6x \;\;\; + 9 + 10ix +30i &+ -25 \end{align}\]

Then remember to gather your units terms.