True or false: The absolute values of a complex number and its complex conjugate are always equal. & WHY?

Answer 1

Let a + bi be your complex number.
Its absolute value is √(a²+b²).
The conjugate of a + bi is a-bi and its absolute
value is also √(a²+b²). So your statement is true.

Answer 2

The absolute value of a complex number a + or - bi is sqrt(a^2 +b^2). You get the same answer.

Another way to look at it is by writing as r*exp(iθ) for a+ib and r*exp(-iθ) for a -ib. The magnitude (or absolute value ) is r teh same for both numbers (the absolute value of exp(iθ) is always 1).

Answer 3

tricky point. query on yahoo and bing. that might help!