Simplify the expression.
(9+4i)^2

Question

Simplify the expression.
(9+4i)^2

mathmale · Answer

Try expanding (9+4x)^2 first.  Then tackle  (9+4i)^2.

Note:  "i" is the imaginary operator:

i=sqrt(-1)

i^2= -1

i^3= -i

i^4=1

zuha · Answer

@mathmale 81+16x?

pooja195 · Answer

"^2" basically means it's written twice  
$$\huge~\rm (9+4i)^2--> (9+4i)(9+4i)$$

pooja195 · Answer

Now just use the Foil method 
Can you tell me what we get once we do that?

zuha · Answer

@pooja195 81+36i+36i+4i^2

zuha · Answer

So basically 81+72i+4i^2

pooja195 · Answer

"^2" basically means it's written twice  
$$\huge~\rm (9+4i)^2--> (9+4i)(9+4i)$$
81+36i+36i+16i^2

zuha · Answer

Ah makes sense, so 81+72i+16i^2?

pooja195 · Answer

Keep in mind that i^2=-1

pooja195 · Answer

"^2" basically means it's written twice  
$$\huge~\rm (9+4i)^2--> (9+4i)(9+4i)$$
81+36i+36i+16(-1)  

Combine the like terms :)  
we got: 
81+36i+36i-16

pooja195 · Answer

Are you stuck?

zuha · Answer

Ah so the i would be removed from 16 as there is as a square, correct?

zuha · Answer

So would it be 81+72i+16?

pooja195 · Answer

not quite 
72i is correct but remember we said i^2=-1  which makes 16i^2=-16
Which would mean we subtract 81-16=?

zuha · Answer

65!

pooja195 · Answer

Yes! :D so whats the answer? :O

zuha · Answer

65+72i

zuha · Answer

That's perfect, thank you!!!

pooja195 · Answer

Perfect  <3  
You're welcome ^_^