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Complex number short question

solve the simultaneous equation
z=w+3i+2
z^2-iw+5-2i=0
Original post by crystalong
solve the simultaneous equation
z=w+3i+2
z^2-iw+5-2i=0


Hi there. What have you tried?
Reply 2
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crystalong
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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
Reply 3
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Zacken
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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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Zacken
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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
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?
Reply 8
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Original post by Student403
Where has your -9 and +5 gone?


-9+4+5=0
Original post by crystalong
-9+4+5=0


Ah :biggrin:
Put your quadratic in the form w^2 + (5i+4)w + 10i = 0 and use the quadratic formula.
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crystalong
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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
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.
(edited 8 years ago)
Reply 13
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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
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.
(edited 8 years ago)
Reply 15
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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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