How can u define zero in complex numbers?

Question

The Set of Real Numbers is a subset of complex numbers. therefore all real numbers are complex numbers..and can be expressed in the form of x+iy = r( cis t) where t is principal amplitude. for zero, x=0=y and r=0 .but the value of 't' is undefined for zero. how can the product of zero and an undefined value become zero?

Answer 1

The problem with using r(cis t) as a coordinate system is, as you have found, there is not a unique way to refer to the origin of the complex plane; however, in spite of this, there is an origin and it is simply 0+0i.

Answer 2

x + iy is the defining form for complex numbers. You don't have a problem there.

Polar coordinates are just coordinates for the points on the plane. They do a good job everywhere except the origin, but they break down there.

Answer 3

0= 0+0*i and in polar cordinates r=0.Angle no needed because if you have the product of two numbers and one has module 0 the product has module 0 and so is 0

Answer 4

No. a complicated form features a real section and an imaginary section. The sq. root of ANY detrimental form is imaginary, as are another issues, jointly with logs of detrimental numbers.