# Complex numbers

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#1
Given that z=a+bi and w=a-bi show that:

a)z+w is always real
b)z-w is always imaginary

Any help appreciated.Thx
0
2 years ago
#2
(Original post by InfinityMist)
Given that z=a+bi and w=a-bi show that:

a)z+w is always real
b)z-w is always imaginary

Any help appreciated.Thx
Have you tried working out z+w and z-w? What did you get?
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#3
yes, z+w =2a and z-w =0
0
2 years ago
#4
(Original post by InfinityMist)
yes, z+w =2a and z-w =0
Do you see why z+w is a real number?

Also z-w is not 0.
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#5
Does z-w= 2bi then. Still not sure why z+w is a real number
0
2 years ago
#6
(Original post by InfinityMist)
Does z-w= 2bi then. Still not sure why z+w is a real number
z+w is a real number because it has no imaginary component. Clearly, it cancels out in the addition.

Similar argument for z-w
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#7
Thanks for the help.
Last edited by InfinityMist; 2 years ago
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