Question Express your answer in the form .
Studdy Solution
STEP 1
What is this asking? We're adding two *complex numbers* and need to write the result in the standard form . Watch out! Don't mix up the real and imaginary parts!
STEP 2
1. Group the real and imaginary terms
2. Add the real parts
3. Add the imaginary parts
4. Combine the results
STEP 3
Let's **rewrite** our expression to **group** the real parts and the imaginary parts together.
This makes it super clear what we need to add!
Remember, the *real part* is the number *without* the , and the *imaginary part* is the number *with* the .
So, we have:
STEP 4
Now, let's **add** those real parts together!
We have and , and when we add them, we get:
So, our **new real part** is !
STEP 5
Next up, the imaginary parts!
We have and .
When we add these together, we get:
Our **new imaginary part** is !
STEP 6
Finally, let's **put it all together**!
We have our **real part**, which is , and our **imaginary part**, which is .
We write the **final answer** in the form , so we get:
STEP 7
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