For z=x+iy๐ง=๐ฅ+๐๐ฆ find the values x๐ฅ and y๐ฆ satisfying 2z1+iโ2zi=52+i2๐ง1+๐โ2๐ง๐=52+๐.
Question
Solution
1. Break Down the Problem
We need to solve the equation: where . This requires simplifying both sides and isolating the variables and .
2. Relevant Concepts
- Substitute .
- Use properties of complex numbers to simplify the equation.
- Set the real and imaginary parts equal to isolate the variables.
3. Analysis and Detail
Step 1: Substitute
Substituting into the equation:
This simplifies to:
Step 2: Simplifying the numerator
So, the numerator becomes:
This gives:
Step 3: Simplifying the denominator
For the denominator: So, it becomes:
Step 4: Set up the equation
Now, rewrite the equation in simpler form:
Step 5: Cross-multiply
Cross-multiplying gives:
Step 6: Equate real and imaginary parts
We can now separate real and imaginary components:
- Real part:
- Imaginary part:
4. Verify and Summarize
Solving the imaginary part:
Now substitute back into the real part: This simplifies to: Multiply through by 3: Combine terms:
Final Answer
Thus, the values of and that satisfy the equation are:
Similar Questions
For z=x+iy๐ง=๐ฅ+๐๐ฆ find the values x๐ฅ and y๐ฆ satisfying 2z1+iโ2zi=52+i2๐ง1+๐โ2๐ง๐=52+๐.
Find the z-score for the value 52, when the mean is 58 and the standard deviation is 9.Group of answer choicesz=-0.78z=-0.74z=0.74z=-0.67
Typing z=2+5i and then conj(z) in MATLAB command line will output :Group of answer choices5+2i252-5i
๐๐ข๐๐๐๐ ๐ ๐กโ๐๐ก ๐กโ๐ ๐โ๐๐๐๐๐ก๐๐๐๐ ๐ก๐๐ ๐๐๐๐ฆ๐๐๐๐๐๐ ๐๐ ๐ ๐๐๐ ๐๐๐ก๐๐๐ฅ ๐ด ๐๐ ๐๐๐ข๐๐ ๐ก๐ ๐๐ ๐(๐) = (๐ - 1)๐ -32 ๐ -43 . ๐โ๐๐ก ๐๐ ๐กโ๐ ๐ ๐๐ง๐ ๐๐ ๐ด?
For the equation ๐=2๐คโ5, complete the table of values below.๐ค2345๐ Submit answer
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