Math Is Fun Forum

shivusuja

Member

Registered: 2006-09-14

Posts: 56

complex number

Please help me out with the below given two sums

1.  For any two complex numbers Z1 and Z2, prove that
     Re (Z1 Z2) = Re Z1  Re Z2 - ImZ1 ImZ2.

2.  If x-iy = √ a-ib ÷ √c-id prove that (x² + y²)² = a² +  b² ÷ c² + d²

Thank you in advance.

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: complex number

for 1.

Last edited by luca-deltodesco (2007-08-21 02:52:17)

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Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: complex number

For 2, can you use the theorem:

Or perhaps this is (in a weird sort of way) what you are trying to prove?

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JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: complex number

2

You can check that

∴

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: complex number

For 2, can you use the theorem:

Why didn’t I think of that before.