Question

(1/2 - 1/4i) (5/6 + 5/6i)

Help me Multiply. Please!

Answer 1

Multiply like you would two factors, then add the real parts and add the imaginary parts.

Answer 2

This is so hard for me. Can you please go through the steps and help me with the answer?

Answer 3

@eSpeX Can you help me with this? This is really hard for me.

Answer 4

Let's confirm, this is your equation, yes? \[(\frac{1}{2}-\frac{1}{4}i)(\frac{5}{6}+\frac{5}{6}i)\]

Answer 5

Yes!

Answer 6

You then foil the two terms like you would (x+2)(x-4)

Answer 7

1/2 * 5/6 ?

Answer 8

Yes

Answer 9

15/6 ?

Answer 10

5/12

Answer 11

You multiply the denominators and the numerators.

Answer 12

Oh! Alright, so far 5/12 ?

Answer 13

Then would it be 5/12 again?

Answer 14

Yes, but you have an i as well so it would be 5/12 i

Answer 15

Would -1/4 i * 5/6 be 60/24i ?

Answer 16

\[\frac{1*5}{4*6}i\]

Answer 17

negative of course.

Answer 18

5/24 i?

Answer 19

Yes

Answer 20

So far 5/12 + 5/12i - 5/24i + 5/24 i^2

Answer 21

Exactly, now recall what 'i' stands for, it is the sqrt of -1, so i^2 is?

Answer 22

5/24(-1) = -5/24?

Answer 23

Precisely.

Answer 24

So would the answer be 5/12 + 5/12i +5/24i - 5/24 ?

Answer 25

You must now combine like terms.

Answer 26

5/12 - 5/24 be 5/24?

Answer 27

No, you would need to give them the same denominator to be able to subtract them. Also, it seems we dropped a sign somewhere, I think it was when you did -1/4i*5/6i, it would have given you -5/24(-1) to end up with 5/24.

Answer 28

So the same Denominator would be 24?

Answer 29

So what would you need to do to 5/12 to get the same denominator? Yes, 24.

Answer 30

Multiply by the GCF?

Answer 31

A common factor yes.

Answer 32

15/24 ?

Answer 33

Is that your conversion or final answer?

Answer 34

My conversion

Answer 35

How did you get it?

Answer 36

multiply and adding?

Answer 37

Okay, so you are saying it is your final answer, because your conversion of 5/12 was 10/24 and you added them together to get 15/24.

Answer 38

Yes.

Answer 39

Okay, now you will do the same thing to your imaginary parts. \[\frac{5}{12}i-\frac{5}{24}i\]

Answer 40

5/24 i ?

Answer 41

Good. So what is your final result?

Answer 42

15/24 - 5/24 i ?

Answer 43

And can you reduce any of those terms?

Answer 44

no

Answer 45

What about 15/24, don't they have a common factor?

Answer 46

5/8

Answer 47

Perfect. Excellent work.

Answer 48

So the final answer is: 5/8 - 5/24 i ?

Answer 49

Indeed it is.

Answer 50

Thank you!!!!

Answer 51

You did all the heavy lifting, but you are certainly welcome.