Complex Vectors

It is not obvious how one would define complex vectors. It is not meaningful to introduce imaginary vectors by just taking the “square root” of a “negative vector”, similar to the way we take the square root of the negative number −1, to arrive at an “imaginary number”. Also the multiplication of a real vector u → ∈ I E → 3 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203702413/2f242b9b-104e-4a03-b478-d3f6577cf44e/content/eq1666.tif"/> by a complex number, e.g., ( a + i b ) u → https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203702413/2f242b9b-104e-4a03-b478-d3f6577cf44e/content/eq1667.tif"/> , does not have an intuitive meaning. We need an approach which is not based on “imaginary vectors”.