Multiply the complex numbers (3+2i)(3-2i)?

Question

Multiply the complex numbers (3+2i)(3-2i)

Answer 1

(3 + 2i) (3 - 2i)

(3 + 2i) * 3 = 9 + 6i
(3 + 2i) * - 2i = - 6i - 4i^2

9 + 6i -6i - 4i^2

Answer: 9 - 4i^2

Solving for i:
(3 + 2i) (3- 2i)
3^2 - 2(i^2)
9 - (-4)
9 + 4
13

Proof:
(3 + 2[13]) (3 - 2[13]) = 9 - 4[13]^2)
(3 + 26) (3 - 26) = 9 - 4[169]
29 * (- 23) = 9 - 676
667 = 667

Answer 2

(3 +2i)(3 - 2i)
It is in the form of (a+b)(a-b), the product of which is a^2 - b^2
So (3 +2i)(3 - 2i) = 3^2 - (2i)^2 = 9 - 4i^2 = 9 - 4(-1) = 9 +4 = 13

Answer 3

Hey there!

Here's the answer.

(3+2i)(3-2i) --> Write the problem.
9+6i-6i-4i^2 --> Use FOIL.
9-4i^2 --> Cancel out the 6i terms.
9-4(-1) --> Recall that i^2=-1.
9+4 --> Multiply -4 and -1.
13 Add 9 and 4.

So the answer is 13.

Hope it helps!

Answer 4

(a+b)(a-b) = a^2 - b^2 ----- Remember this formula. It is very useful.


(3+2i)(3-2i)
= 3^2 - (2i)^2
= 9 - (-4)
= 9 + 4
= 13

Answer 5

(3+2i)(3-2i)=9-6i+6i+4=9+4=13
The answer can’t be 5, since i*i=-1 and as you know there’s a -2*2=-4.
Therefore -4*-1=4 which proves my answer.

Answer 6

1) Factor as you normally would to get 15-10i-18i+12i^2, which simplifies to 15-28i+12(-1) since i^2=-1. Final answer is 3-28i. 2) Multiply the whole thing by the conjugate of the denominator, 4+5i. You will get 2i(4+5i)/4+5i(4-5i). Just simplify and you will have your answer.

Answer 7

(3+2i)(3-2i)
= 9 + 6i - 6i - 4i²

Recall that i² = -1
= 9 - (4)(-1)
= 9 + 4
= 13

Answer 8

Use the FOIL rule and i² = -1.
You get 9 +6i-6i -4i² = 9 + 4 = 13.

Answer 9

3*3-2*3*2i+(2i)2=(2i)2-12i+9;

* (2i)2 means (2i)squared