Studdy AI Logo
Math  /  Algebra

QuestionFind the values of xx and yy in each equation below:
9. x+yi=2−9ix+y i=2-9 i
10. 1+10i=(x−4)+2yi1+10 i=(x-4)+2 y i

Studdy Solution

STEP 1

What is this asking? We're looking to find the values of x x and y y that make these equations true. Watch out! Don't forget to match the real parts with the real parts and the imaginary parts with the imaginary parts!

STEP 2

1. Match real and imaginary parts for the first equation
2. Solve for x x and y y in the first equation
3. Match real and imaginary parts for the second equation
4. Solve for x x and y y in the second equation

STEP 3

Alrighty! Let's start with the first equation: x+yi=2−9i x + y i = 2 - 9 i .
The key here is to **match the real parts** and **match the imaginary parts** separately.
So, we have:
- Real part: x=2 x = 2 - Imaginary part: y=−9 y = -9

STEP 4

Since we've already matched the parts, we can directly say:
- x=2 x = 2 - y=−9 y = -9
And that's it for the first equation!
Easy peasy!

STEP 5

Now, let's tackle the second equation: 1+10i=(x−4)+2yi 1 + 10 i = (x - 4) + 2 y i .
Again, we need to **match the real parts** and **match the imaginary parts**.
So, we get:
- Real part: 1=x−4 1 = x - 4 - Imaginary part: 10=2y 10 = 2y

STEP 6

Let's solve these equations step by step:
For the real part: \[ 1 = x - 4 $ **Add 4** to both sides to solve for \( x \): \[ x = 5 $
For the imaginary part: \[ 10 = 2y $ **Divide by 2** to solve for \( y \): \[ y = 5 $
And there we have it for the second equation!

STEP 7

For the first equation, the values are x=2 x = 2 and y=−9 y = -9 .
For the second equation, the values are x=5 x = 5 and y=5 y = 5 .

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord