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# Complex number short question watch

1. solve the simultaneous equation
z=w+3i+2
z^2-iw+5-2i=0
2. (Original post by crystalong)
solve the simultaneous equation
z=w+3i+2
z^2-iw+5-2i=0
Hi there. What have you tried?
3. (Original post by Kvothe the arcane)
Hi there. What have you tried?
i ended up with w^2+4w+(5w+10)=0
4. (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?
5. (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
6. (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?
7. (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
8. (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?
9. (Original post by Student403)
Where has your -9 and +5 gone?
-9+4+5=0
10. (Original post by crystalong)
-9+4+5=0
Ah
11. Put your quadratic in the form w^2 + (5i+4)w + 10i = 0 and use the quadratic formula.
12. (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
13. (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.
14. (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
15. (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.
16. (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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