# What is/are the complex numbers whose modulus is √25? A complex number is a number of the form `a+bi` where `a,binRR` (a,b are real numbers) and `i=sqrt(-1)` .

The modulus of a complex number `|a+bi|=sqrt(a^2+b^2)` is the distance of the point from the origin in the Argand plane (the complex plane; the horizontal axis is the real numbers, while...

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A complex number is a number of the form `a+bi` where `a,binRR` (a,b are real numbers) and `i=sqrt(-1)` .

The modulus of a complex number `|a+bi|=sqrt(a^2+b^2)` is the distance of the point from the origin in the Argand plane (the complex plane; the horizontal axis is the real numbers, while the vertical axis is the imaginary numbers)

If the modulus of `z=a+bi` is `sqrt(25)` , then we have `a^2+b^2=25` .

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Thus the set of numbers in the complex plane with modulus `sqrt(25)` is the circle, centered at the origin with radius 5, in the complex plane.

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Some example points include `3+4i,-3+4i` , etc...

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