Math Is Fun Forum

{7/3}

Member

Registered: 2013-02-11

Posts: 210

an easy question

I can't see any way to solve this
prove,a+bi=c+di implies a=b and c=d

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There are 10 kinds of people in the world,people who understand binary and people who don't.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: an easy question

That is not a true statement.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: an easy question

I expect {7/3} meant

a = c and b = d

I think it is axiomatic rather than provable ... but as ever, it depends on the initial axioms chosen.

Bob

researching .....

LATER:

Looks like it isn't an axiom.  hhmmm.

So try a-c = i(d-b) => i = (a-c)/d-b)  =><= i is not real unless d = b

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: an easy question

I do not think so.

a+bi=c+di
implies
a-c=(b-d)*i

If (b-d)!=0, then a-c is complex, which is not possible. So, b-d must be equal to 0, i.e. b must equal d. That further implies that a-c=0, i.e. a=c.

Last edited by anonimnystefy (2013-07-01 20:06:17)

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

{7/3}

Member

Registered: 2013-02-11

Posts: 210

Re: an easy question

thanks.

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There are 10 kinds of people in the world,people who understand binary and people who don't.