QuestionSimplify. $-(0.3+8.2 i)-(-2.8+2.3 i)$
Write your answer in the form a + bi. $\square$

Studdy Solution

STEP 1

What is this asking? We're subtracting one complex number from another, and we need to present the result in the standard a + bi format. Watch out! Don't forget to distribute the negative sign correctly when subtracting the second complex number!

STEP 2

1. Distribute the negative signs
2. Group the real and imaginary parts
3. Simplify and write in standard form

STEP 3

Alright, let's kick things off by distributing those negative signs!
We have $-(0.3 + 8.2i) - (-2.8 + 2.3i)$ .
Distributing the first negative sign gives us $-0.3 - 8.2i$ .
Distributing the second negative sign changes the sign of each term inside the parentheses, giving us $-(-2.8) + (-2.3i)$ , which simplifies to $+2.8 - 2.3i$ .

STEP 4

So, our expression now looks like this: $-0.3 - 8.2i + 2.8 - 2.3i$ .
Much better!

STEP 5

Now, let's group our friends!
We'll put the real parts together and the imaginary parts together.
Our real parts are $-0.3$ and $+2.8$ , and our imaginary parts are $-8.2i$ and $-2.3i$ .

STEP 6

Grouping them gives us $(-0.3 + 2.8) + (-8.2i - 2.3i)$ .
This makes things much clearer!

STEP 7

Time to simplify!
Adding the real parts, $-0.3 + 2.8$ , gives us $2.5$ .
Adding the imaginary parts, $-8.2i - 2.3i$ , gives us $-10.5i$ .

STEP 8

Putting it all together, we get $2.5 - 10.5i$ .
And there you have it!
Our answer is in the beautiful a + bi format.

STEP 9

$2.5 - 10.5i$

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