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    solve the simultaneous equation
    z=w+3i+2
    z^2-iw+5-2i=0
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    (Original post by crystalong)
    solve the simultaneous equation
    z=w+3i+2
    z^2-iw+5-2i=0
    Hi there. What have you tried?
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    (Original post by Kvothe the arcane)
    Hi there. What have you tried?
    i ended up with w^2+4w+(5w+10)=0
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    (Original post by crystalong)
    i ended up with w^2+4w+(5w+10)=0
    Which is a quadratic. Do you know how to solve a quadratic equation?
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    (Original post by Zacken)
    Which is a quadratic. Do you know how to solve a quadratic equation?
    w^2+4w+(5w+10)i=0
    the i behind
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    (Original post by crystalong)
    w^2+4w+(5w+10)i=0
    the i behind
    How did you get that? Doesn't look right - mind posting your working?
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    (Original post by Zacken)
    How did you get that? Doesn't look right - mind posting your working?
    (w+3i+2)^2-iw+5-2i=0
    w^2+2w(3i+2)+(3i+2)^2-iw+5-2i=0
    w^2+6wi+4w-9+12i+4-iw+5-2i=0
    w^2+4w+(5w+10)i=0
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    (Original post by crystalong)
    (w+3i+2)^2-iw+5-2i=0
    w^2+2w(3i+2)+(3i+2)^2-iw+5-2i=0
    w^2+6wi+4w-9+12i+4-iw+5-2i=0
    w^2+4w+(5w+10)i=0
    Where has your -9 and +5 gone?
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    (Original post by Student403)
    Where has your -9 and +5 gone?
    -9+4+5=0
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    (Original post by crystalong)
    -9+4+5=0
    Ah
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    Put your quadratic in the form w^2 + (5i+4)w + 10i = 0 and use the quadratic formula.
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    (Original post by NamelessPersona)
    Put your quadratic in the form w^2 + (5i+4)w + 10i = 0 and use the quadratic formula.
    tried it but can't get the ans which is w=-2-4i and z=-i
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    (Original post by crystalong)
    tried it but can't get the ans which is w=-2-4i and z=-i
    Can you show your working please? I seem to get the correct solution, indicating that you have gone wrong somewhere. Also, there are two values for w, and therefore two values for z.
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    (Original post by NamelessPersona)
    Can you show your working please? I seem to get the correct solution, indicating that you have gone wrong somewhere. Also, there are two values for w, and therefore two values for z.
    w= (-5i-4+-square root of (5i+4)^2-4(10i))/2
    = (-5i-4+-square root of -9)/2
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    (Original post by crystalong)
    w= (-5i-4+-square root of (5i+4)^2-4(10i))/2
    = (-5i-4+-square root of -9)/2
    w = [-5i - 4 +- sqrt(-9)]/2. Simplify the numerator by evaluating the square root and you will get your two values for w.
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    (Original post by NamelessPersona)
    w = [-5i - 4 +- sqrt(-9)]/2. Simplify the numerator by evaluating the square root and you will get your two values for w.
    got it, thanks!
 
 
 
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