Question

write the expression as a complex number in standard form.
(10-4i)(3+4i)

Answer 1

Use FOIL to multiply together like we did yesterday:
(10 - 4i)(3 + 4i) =
10 * 3 + 10 * 4i - 4i * 3 - 4i * 4i
Now do all 4 multiplications

Answer 2

10*3=30
10*4i=40i
4i*3=12i
4i*4i=16i

Answer 3

Almost. Look at the last one:
10*3=30
10*4i=40i
4i*3=12i
4i*4i=16i^2 = 16 * (-1) = -16

Answer 4

so -16 how do we put it all together

Answer 5

10 * 3 + 10 * 4i - 4i * 3 - 4i * 4i =
30 + 40i - 12i - (-16)

Answer 6

10 * 3 + 10 * 4i - 4i * 3 - 4i * 4i =
30 + 40i - 12i - (-16) =
30 + 28i + 16 =
46 + 28i

Answer 7

5/1+2i

Answer 8

You mean this, right?

Answer 9

yeah

Answer 10

You need to multiply the numerator and denominator by the complex conjugate of the denominator.

Answer 11

Can you write the complex conjugate of the denominator?

Answer 12

1-2i

Answer 13

Right. Now we need to multiply.