Pre-Algebra Examples

Solve for z |z|=|z-1-i|
Step 1
Rewrite the equation as .
Step 2
Rewrite the absolute value equation as four equations without absolute value bars.
Step 3
After simplifying, there are only two unique equations to be solved.
Step 4
Solve for .
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Step 4.1
Move all terms containing to the left side of the equation.
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Step 4.1.1
Subtract from both sides of the equation.
Step 4.1.2
Combine the opposite terms in .
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Step 4.1.2.1
Subtract from .
Step 4.1.2.2
Subtract from .
Step 4.2
Since , there are no solutions.
No solution
No solution
Step 5
Solve for .
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Step 5.1
Move all terms containing to the left side of the equation.
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Step 5.1.1
Add to both sides of the equation.
Step 5.1.2
Add and .
Step 5.2
Move all terms not containing to the right side of the equation.
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Step 5.2.1
Add to both sides of the equation.
Step 5.2.2
Add to both sides of the equation.
Step 5.3
Divide each term in by and simplify.
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Step 5.3.1
Divide each term in by .
Step 5.3.2
Simplify the left side.
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Step 5.3.2.1
Cancel the common factor of .
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Step 5.3.2.1.1
Cancel the common factor.
Step 5.3.2.1.2
Divide by .
Step 6
List all of the solutions.