SOLUTION: Solve for ϵC:
|z|-z=4+3i
Could you please show the a step by step solution, as i am a bit confused by this question and dont really know where to start. By the way the "
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Question 917402: Solve for ϵC:
|z|-z=4+3i
Could you please show the a step by step solution, as i am a bit confused by this question and dont really know where to start. By the way the "C" is kind of outlined like the letter "R" for real value.
Thank you in advance :)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i believe C means the set of complex numbers, just like R means the set of real numbers.
your equation is:
add z to both sides of this equation to get:
solve this like any other absolute value equation.
when the expression inside the absolute value sign is positive, the equation of becomes:
subtract z from both sides of this equation and you get:
the variable disappeared and the resulting equation is not true, so z >= 0 has no solution which means that z cannot be greater than or equal to 0.
when the expression inside the absolute value sign is negative, the equation of } becomes:
simplify to get:
add z to both sides of this equation to get:
divide both sides of this equation by 2 to get:
that's your solution.
to see if that makes sense, replace z in your original equation with and see if the original equation is valid.
original equation is
when , original equation of becomes:
}
by the basic definition of absolute value,
this makes your equation of:
become:
which becomes:
which becomes:
which is true.
this confirms the solution is good.
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