Math / Algebra

QuestionSimplify. $(8+14 i)-(12 i-20)-(-7+10 i)$
Write your answer in the form a + bi. $\square$ Submit

Studdy Solution

STEP 1

What is this asking? We're taking a somewhat messy expression with real and imaginary numbers, and we want to simplify it into the standard a + bi form, where a is the real part and b is the imaginary part. Watch out! Be super careful with those minus signs in front of the parentheses – they can be tricky little things!
Don't forget to distribute them correctly.

STEP 2

1. Distribute the minus signs
2. Group like terms
3. Simplify and write in standard form

STEP 3

Alright, let's kick things off by tackling those minus signs!
We have $(8 + 14i) - (12i - 20) - (-7 + 10i)$ .
Remember, a minus sign in front of parentheses means we multiply each term inside by $-1$ .

STEP 4

So, distributing the first minus sign gives us $8 + 14i - 12i + 20$ .
See how the $-20$ turned into a $+20$ ?
That's the magic of distribution!

STEP 5

Now, let's distribute the second minus sign: $8 + 14i - 12i + 20 + 7 - 10i$ .
Again, notice how $-7$ became $+7$ and $+10i$ became $-10i$ .

STEP 6

Now, let's gather our friends!
We'll group the real numbers together and the imaginary numbers together.
We have $8$ , $20$ , and $7$ as our real numbers, and $14i$ , $-12i$ , and $-10i$ as our imaginary numbers.

STEP 7

Grouping them gives us $(8 + 20 + 7) + (14i - 12i - 10i)$ .
See how much neater that looks?

STEP 8

Time to combine and conquer!
Adding the real numbers, $8 + 20 + 7$ , gives us $35$ .

STEP 9

Adding the imaginary numbers, $14i - 12i - 10i$ , gives us $-8i$ .
Remember, we're just adding the coefficients of i.

STEP 10

Putting it all together, we get $35 - 8i$ .
Boom! That's our answer in the beautiful a + bi form.

STEP 11

$35 - 8i$

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QuestionSimplify. $(8+14 i)-(12 i-20)-(-7+10 i)$
Write your answer in the form a + bi. $\square$ Submit

Studdy Solution

STEP 1

STEP 2

1. Distribute the minus signs
2. Group like terms
3. Simplify and write in standard form

STEP 3

Alright, let's kick things off by tackling those minus signs!
We have $(8 + 14i) - (12i - 20) - (-7 + 10i)$ .
Remember, a minus sign in front of parentheses means we multiply each term inside by $-1$ .

STEP 4

So, distributing the first minus sign gives us $8 + 14i - 12i + 20$ .
See how the $-20$ turned into a $+20$ ?
That's the magic of distribution!

STEP 5

Now, let's distribute the second minus sign: $8 + 14i - 12i + 20 + 7 - 10i$ .
Again, notice how $-7$ became $+7$ and $+10i$ became $-10i$ .

STEP 6

Now, let's gather our friends!
We'll group the real numbers together and the imaginary numbers together.
We have $8$ , $20$ , and $7$ as our real numbers, and $14i$ , $-12i$ , and $-10i$ as our imaginary numbers.

STEP 7

Grouping them gives us $(8 + 20 + 7) + (14i - 12i - 10i)$ .
See how much neater that looks?

STEP 8

Time to combine and conquer!
Adding the real numbers, $8 + 20 + 7$ , gives us $35$ .

STEP 9

Adding the imaginary numbers, $14i - 12i - 10i$ , gives us $-8i$ .
Remember, we're just adding the coefficients of i.

STEP 10

Putting it all together, we get $35 - 8i$ .
Boom! That's our answer in the beautiful a + bi form.

STEP 11

$35 - 8i$

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QuestionSimplify. (8+14i)−(12i−20)−(−7+10i)(8+14 i)-(12 i-20)-(-7+10 i)(8+14i)−(12i−20)−(−7+10i)Write your answer in the form a + bi. □\square□ Submit

Studdy Solution

STEP 1

STEP 2

1. Distribute the minus signs2. Group like terms3. Simplify and write in standard form

STEP 3

Alright, let's **kick things off** by tackling those minus signs!We have (8+14i)−(12i−20)−(−7+10i)(8 + 14i) - (12i - 20) - (-7 + 10i)(8+14i)−(12i−20)−(−7+10i).Remember, a minus sign in front of parentheses means we multiply each term inside by −1-1−1.

STEP 4

So, distributing the first minus sign gives us 8+14i−12i+208 + 14i - 12i + 208+14i−12i+20.See how the −20-20−20 turned into a +20+20+20?That's the magic of distribution!

STEP 5

Now, let's distribute the second minus sign: 8+14i−12i+20+7−10i8 + 14i - 12i + 20 + 7 - 10i8+14i−12i+20+7−10i.Again, notice how −7-7−7 became +7+7+7 and +10i+10i+10i became −10i-10i−10i.

STEP 6

Now, let's **gather our friends**!We'll group the real numbers together and the imaginary numbers together.We have 888, 202020, and 777 as our real numbers, and 14i14i14i, −12i-12i−12i, and −10i-10i−10i as our imaginary numbers.

STEP 7

Grouping them gives us (8+20+7)+(14i−12i−10i)(8 + 20 + 7) + (14i - 12i - 10i)(8+20+7)+(14i−12i−10i).See how much neater that looks?

STEP 8

Time to **combine and conquer**!Adding the real numbers, 8+20+78 + 20 + 78+20+7, gives us 353535.

STEP 9

Adding the imaginary numbers, 14i−12i−10i14i - 12i - 10i14i−12i−10i, gives us −8i-8i−8i.Remember, we're just adding the coefficients of *i*.

STEP 10

Putting it all together, we get 35−8i35 - 8i35−8i.Boom! That's our answer in the beautiful *a* + *bi* form.

STEP 11

35−8i35 - 8i35−8i

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QuestionSimplify. $(8+14 i)-(12 i-20)-(-7+10 i)$
Write your answer in the form a + bi. $\square$ Submit

1. Distribute the minus signs
2. Group like terms
3. Simplify and write in standard form

Alright, let's kick things off by tackling those minus signs!
We have $(8 + 14i) - (12i - 20) - (-7 + 10i)$ .
Remember, a minus sign in front of parentheses means we multiply each term inside by $-1$ .

So, distributing the first minus sign gives us $8 + 14i - 12i + 20$ .
See how the $-20$ turned into a $+20$ ?
That's the magic of distribution!

Now, let's distribute the second minus sign: $8 + 14i - 12i + 20 + 7 - 10i$ .
Again, notice how $-7$ became $+7$ and $+10i$ became $-10i$ .

Now, let's gather our friends!
We'll group the real numbers together and the imaginary numbers together.
We have $8$ , $20$ , and $7$ as our real numbers, and $14i$ , $-12i$ , and $-10i$ as our imaginary numbers.

Grouping them gives us $(8 + 20 + 7) + (14i - 12i - 10i)$ .
See how much neater that looks?

Time to combine and conquer!
Adding the real numbers, $8 + 20 + 7$ , gives us $35$ .

Adding the imaginary numbers, $14i - 12i - 10i$ , gives us $-8i$ .
Remember, we're just adding the coefficients of i.

Putting it all together, we get $35 - 8i$ .
Boom! That's our answer in the beautiful a + bi form.

$35 - 8i$