Math  /  Algebra

QuestionSimplify. 6.2i(4.94.9i)(6.86.9i)-6.2 i-(-4.9-4.9 i)-(6.8-6.9 i)
Write your answer in the form a+bi\mathrm{a}+\mathrm{bi}. \square ii

Studdy Solution

STEP 1

What is this asking? We're asked to simplify a complex number expression and write the answer in the standard form a+bia + bi, where aa is the real part and bb is the imaginary part. Watch out! Be careful with the signs when distributing the negative sign across parentheses!

STEP 2

1. Distribute the negative signs.
2. Regroup the terms.
3. Simplify the real part.
4. Simplify the imaginary part.

STEP 3

Alright, let's **kick things off** by distributing those negative signs!
We have 6.2i(4.94.9i)(6.86.9i)-6.2i - (-4.9 - 4.9i) - (6.8 - 6.9i).
Distributing the negative sign across the parentheses gives us 6.2i+4.9+4.9i6.8+6.9i-6.2i + 4.9 + 4.9i - 6.8 + 6.9i.
Remember, multiplying by 1-1 flips the signs!

STEP 4

Now, let's **regroup** our terms to put the real parts together and the imaginary parts together.
This gives us 4.96.8+4.9i6.2i+6.9i4.9 - 6.8 + 4.9i - 6.2i + 6.9i.
Think of it like sorting apples and oranges – we want all the apples together and all the oranges together!

STEP 5

Let's **tackle the real part** first: 4.96.84.9 - 6.8.
This gives us 1.9-1.9.
So, our real part is 1.9-1.9.

STEP 6

Now for the **imaginary part**: 4.9i6.2i+6.9i4.9i - 6.2i + 6.9i.
Combining these terms gives us (4.96.2+6.9)i(4.9 - 6.2 + 6.9)i.
Calculating 4.96.2+6.94.9 - 6.2 + 6.9 gives us 5.65.6.
So, our imaginary part is 5.6i5.6i.

STEP 7

Our **final answer** is 1.9+5.6i-1.9 + 5.6i.
We've successfully simplified the complex number expression!

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