SOLUTION: Can someone please help. Simplify the expression so that it is in the form (a + bi).
2/3-{ { {sqrt ( -1 ) } } } / { { { sqrt( -4 ) } } } + 1/2
Question 1133897: Can someone please help. Simplify the expression so that it is in the form (a + bi).
2/3-{ { {sqrt ( -1 ) } } } / { { { sqrt( -4 ) } } } + 1/2
Found 4 solutions by Boreal, MathLover1, MathTherapy, greenestamps:Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website! From how it appears, this is (2/3)-i/(2i+1/2)
rewrite as (2/3)-i/((1/2)+2i)
multiply top and bottom by conjugate ((1/2)- 2i)
numerator is ((2/3)+i)((1/2-2i)=(1/3)-(4/3)i+(1/2)i-2i^2=(1/3)-(5/6)i+2 or (7/3)-(5/6)i
denominator is (1/4)+4 or 17/4
This is [4(7/3)-(10/3)i]/17 Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website! in the form :
------ Substituting ======> =======> ------ Multiplying numerator and denominator by the conjugate of 1 + 4i, or by 1 - 4i ------ Replacing <======== CORRECT ANSWER
You have three responses, one of which contains the right answer; the other two both contain computational errors and so end up with wrong answers.
The three responses show different ways of evaluating the expression; indeed many paths are possible. The one thing that I would suggest, looking at the three responses, is to always write your complex numbers in a+bi form. Performing operations with complex numbers in bi+a form (or with some numbers in one form and others in the other form) is prone to errors.
So here is what I would do with this problem....
= [put the denominator in a+bi form]
= [multiply numerator and denominator by the conjugate of the denominator]
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