Math / Algebra

QuestionSimplify. $\begin{array}{c} (6-i)+(5-8 i) \\ {[?]+i} \end{array}$

Studdy Solution

STEP 1

What is this asking? We're adding two complex numbers and want to write the result in the standard form $a + bi$ , where $a$ is the real part and $b$ is the imaginary part. Watch out! Don't forget that $i$ is not a variable, it's the imaginary unit defined as $\sqrt{-1}$ .
Keep the real and imaginary parts separate!

STEP 2

1. Group the Real and Imaginary Parts
2. Simplify the Expression

STEP 3

Alright, let's rewrite our expression to group the real parts and the imaginary parts together!
This makes it super clear what we're adding.
So, we have $(6 - i) + (5 - 8i)$ .
We can regroup this as $(6 + 5) + (-i - 8i)$ .
We're using the associative property of addition here, which means we can change the grouping of the numbers being added without changing the sum.
Pretty neat, huh?

STEP 4

Now, let's simplify!
Adding the real parts, $6 + 5$ gives us 11.
Awesome!

STEP 5

Next, let's tackle the imaginary parts.
We have $-i - 8i$ .
Remember, $-i$ is the same as $-1 \cdot i$ .
So, we can rewrite this as $-1i - 8i$ .
Now, we can factor out the $i$ , giving us $(-1 - 8)i$ .

STEP 6

Finally, $-1 - 8$ gives us -9.
So, the imaginary part simplifies to $-9i$ .

STEP 7

Putting it all together, our simplified complex number is $11 - 9i$ .
Boom!

STEP 8

Our final answer is $11 - 9i$ , where the real part is $11$ and the imaginary part is $-9$ .

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QuestionSimplify. $\begin{array}{c} (6-i)+(5-8 i) \\ {[?]+i} \end{array}$

Studdy Solution

STEP 1

STEP 2

1. Group the Real and Imaginary Parts
2. Simplify the Expression

STEP 3

STEP 4

Now, let's simplify!
Adding the real parts, $6 + 5$ gives us 11.
Awesome!

STEP 5

Next, let's tackle the imaginary parts.
We have $-i - 8i$ .
Remember, $-i$ is the same as $-1 \cdot i$ .
So, we can rewrite this as $-1i - 8i$ .
Now, we can factor out the $i$ , giving us $(-1 - 8)i$ .

STEP 6

Finally, $-1 - 8$ gives us -9.
So, the imaginary part simplifies to $-9i$ .

STEP 7

Putting it all together, our simplified complex number is $11 - 9i$ .
Boom!

STEP 8

Our final answer is $11 - 9i$ , where the real part is $11$ and the imaginary part is $-9$ .

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QuestionSimplify. (6−i)+(5−8i)[?]+i\begin{array}{c} (6-i)+(5-8 i) \\ {[?]+i} \end{array}(6−i)+(5−8i)[?]+i​

Studdy Solution

STEP 1

STEP 2

1. Group the Real and Imaginary Parts2. Simplify the Expression

STEP 3

STEP 4

Now, let's **simplify**!Adding the **real parts**, 6+56 + 56+5 gives us **11**.Awesome!

STEP 5

Next, let's tackle the **imaginary parts**.We have −i−8i-i - 8i−i−8i.Remember, −i-i−i is the same as −1⋅i-1 \cdot i−1⋅i.So, we can **rewrite** this as −1i−8i-1i - 8i−1i−8i.Now, we can **factor out** the iii, giving us (−1−8)i(-1 - 8)i(−1−8)i.

STEP 6

Finally, −1−8-1 - 8−1−8 gives us **-9**.So, the imaginary part simplifies to −9i-9i−9i.

STEP 7

Putting it all together, our simplified complex number is 11−9i11 - 9i11−9i.Boom!

STEP 8

Our final answer is 11−9i11 - 9i11−9i, where the **real part** is 111111 and the **imaginary part** is −9-9−9.

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QuestionSimplify. $\begin{array}{c} (6-i)+(5-8 i) \\ {[?]+i} \end{array}$

1. Group the Real and Imaginary Parts
2. Simplify the Expression

Now, let's simplify!
Adding the real parts, $6 + 5$ gives us 11.
Awesome!

Next, let's tackle the imaginary parts.
We have $-i - 8i$ .
Remember, $-i$ is the same as $-1 \cdot i$ .
So, we can rewrite this as $-1i - 8i$ .
Now, we can factor out the $i$ , giving us $(-1 - 8)i$ .

Finally, $-1 - 8$ gives us -9.
So, the imaginary part simplifies to $-9i$ .

Putting it all together, our simplified complex number is $11 - 9i$ .
Boom!

Our final answer is $11 - 9i$ , where the real part is $11$ and the imaginary part is $-9$ .