If two complex numbers are equal, say a + ib, c + id, does it imply that a = c and b = d ? Thanks in advance.

Of course ... I don''t see why not and I''d be surprised if someone could prove otherwise.

Well, that''s the definition of the equality of complex numbers. They are equal iff the real and the imaginary parts are equal.

Be careful with the absolute value of complex numbers, because if

abs(a+bi)=abs(c+di)

it doesn''t mean abs(a)=abs(c). It could, but take for example the case of abs(3+4i)=abs(0+5i)
This is true, and is obvious if you graph it on the complex plane. (Try it if you have a calculator which can handle imaginary numbers.) Another example is abs(0+1i)=1 (or abs(1+0i), if you want the abs() on both sides)

Complex numbers are cool, aren''t they?

So what is abs(a+bi)? sqrt(a^2+b^2)?

The symbol is the absolute value symbol, but I think people usually call it magnitude, just like in standard vectors. And yes, the formula is sqrt(a^2+b^2).

Imaginary space is a vector space with extra ops. everything you know about vectors has to apply to imaginary numbers if that helps. that usually gets people going faster. now your knowledge of vectors can help you =)

> The symbol is the absolute value symbol, but I think people
> usually call it magnitude, just like in standard vectors.

The usual term is ''modulus''. see here for more info and references.

Interesting; I`ve always heard iot referred to as the magnitude, with modulus referring to remainder after integer division

Bugle4d

Everything I have ever seen dealing with vectors has shown magnitude as a set of double bars, i.e. ||< a,b >||=sqrt(a² + b²). I always assumed people used single bars just as shorthand when they were writing it. As for the complex numbers... one day I'll get around to learning more about those .

ewen

[edited by - echeslack on May 7, 2002 6:12:26 PM]