Let $z = x + yi$ and $w = u + vi$ be two given complex numbers. State, in terms of vectors,

Question

Let $z = x + yi$ and $w = u + vi$ be two given complex numbers. State, in terms of vectors, the interpretation of the following operations, i.e., $z + w$; $z - w$; $\lambda z$, where $\lambda$ is a positive real number; and $\mu z$, where $\mu$ is a negative real number.

Accepted Answer

(a) $\binom{x+u}{y+v}=\mathbf z+\mathbf w$ (b) $\binom{x-u}{y-v}=\mathbf z-\mathbf w=\overrightarrow{WZ}$ (c) $\lambda\mathbf z$: same direction, length multiplied by $\lambda$ (d) $\mu\mathbf z$: opposite direction, length multiplied by $|\mu|$

Geometric interpretation of arithmetic operations

Geometric interpretation of arithmetic operations

Solution:

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