Are complex numbers vectors?|Mathematics|Sarim Khan

[nirmankhan]

Complex numbers aren't vectors. Cause they don't change their real and imaginary axis. Like 1+2i is 1+2i no matter how you look at it. But a vector's components transforms if your change the coordinates. This is the defining property of vectors.

[yashvantkumar]

Yes. complex number can be treat as vector because every points in vector space represent a vectors corresponding to these points.without the matter of vector space is real or complex.

[anomalous]

Complex Number is a field. And yes it can be thought as a vectorspace over 1 dimensional complex field.

[passion]

Yes complex numbers are vectors. This is a statement from standard mathematical books and due to this magnitude and direction of the complex numbers, we call them as vectors. Some mathematicians call complex numbers as dual natured, only due to the dual nature of complex numbers to behave as vectors and mathematical numbers. That's why you'll never see the product of 2 complex numbers written as Z×Z' or Z•Z' as it shows cross product and dot product as in vectors. Another important thing is that the conjugate of a complex number, as we know is represented with a bar over the number, this representation has NO connection with the vectors. So, to conclude your answer, complex numbers have a dual nature, as vectors and as mathematical numbers.

[EXPECTANT_JEE_]

If i say so, Complex numbers can be thought of as vectors in the complex plane, where the real part represents movement along the x-axis and the imaginary part represents movement along the y-axis. So, in a sense, yes, complex numbers can be interpreted as vectors in a two-dimensional space.

[nitinverma]

Take a cross product of two context number .. n let me know what is perpendicular to complex plane??

[Demolisher]

Bhai agar complex numbers vectors hote toh hum unhe vectors ke Saath padte, Lekin Cno ko 11th mei padhaya jaata hai, and vectors ko 12th mei ( in maths), but to make them easy to understand, they are represented on an argand plane for explaining stuff like the triangular inequality, angle bisector, equation of circle etc, so complex numbers are not vectors however they are analogous to vectors

[tusharhalder]

More generally "The set of complex numbers over the field of real numbers form a 2-dimensional vector space." By thr way your knowledge is phenomenal keep posing good questions like this! Keep going brother ❤

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