Complex Numbers

[Aladdin]

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Questions :

1) The complex number : u = 1 + 2i is the 4th root of : a)m=-7-24i , b) -7+24i , c)7-24i

2) If z1 and z2 are the roots of the equation : z^2 +3iz +2+2i=0, then :

a) |z1|+|z2|=3 , b)arg(z1+z2)=pi/2+2kpi , c) argz1 + argz2 = pi/4+2kpi .

Thanks

 

[Deleted member 4993]

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Questions :

1) The complex number : u = 1 + 2i is the 4th root of : a)m=-7-24i , b) -7+24i , c)7-24i

2) If z1 and z2 are the roots of the equation : z^2 +3iz +2+2i=0, then :

a) |z1|+|z2|=3 , b)arg(z1+z2)=pi/2+2kpi , c) argz1 + argz2 = pi/4+2kpi .

Thanks

Come on Aladdin - you know the drill - where is your work - say "open Sesemi"....

(1 +i2)[sup:kh186nab]4[/sup:kh186nab] = [(1+i2)[sup:kh186nab]2[/sup:kh186nab]][sup:kh186nab]2[/sup:kh186nab] = [1-4+4i][sup:kh186nab]2[/sup:kh186nab] = [-3+4i][sup:kh186nab]2[/sup:kh186nab] = 9 + (4i)[sup:kh186nab]2[/sup:kh186nab] + 2 * (-3) * 4i = ????

.

 

[Aladdin]

Come on Aladdin - you know the drill - where is your work - say "open Sesemi"....

(1 +i2)[sup:f4ov5idu]4[/sup:f4ov5idu] = [(1+i2)[sup:f4ov5idu]2[/sup:f4ov5idu]][sup:f4ov5idu]2[/sup:f4ov5idu] = [1-4+4i][sup:f4ov5idu]2[/sup:f4ov5idu] = [-3+4i][sup:f4ov5idu]2[/sup:f4ov5idu] = 9 + (4i)[sup:f4ov5idu]2[/sup:f4ov5idu] + 2 * (-3) * 4i = ????

I was about to do this approach , you're Khan I was to quick to add the question and post it here. . .

1) The correct answer is a).

For the second question :
z^2 +3iz +2+2i=0

Discriminant = delta = -9 - 4(2+2i)
= -9 -8 -8i
= -17 -8i
So to continue I must get the square root -17-8i or is there any trick I can do . . .