Representation of complex numbers in the plane
Write the associated vector of the following complex numbers needed to give their representation: $ \ 3+5i, \ \sqrt{7}-9i, \ \dfrac{4}{7}i, \ \dfrac{\sqrt{4}}{5} $
We must only write the coefficient of the real part and that of the imginary part. This is to identify $a$ and $b$ from a complex number given in its binomic form.
$ 3+5i \ \Rightarrow \ (a,b)=(3,5)$
$ \sqrt{7}-9i \ \Rightarrow \ (a,b)=(\sqrt{7},-9)$
$ \dfrac{4}{7}i \ \Rightarrow \ (a,b)=(0,\dfrac{4}{7})$
$ \dfrac{\sqrt{4}}{5} \ \Rightarrow \ (a,b)=(\dfrac{\sqrt{4}}{5},0)$
$(3,5), \ (\sqrt{7},-9), \ (0,\dfrac{4}{7}), \ (\dfrac{\sqrt{4}}{5},0)$.
Write the vector associated with the conjugate of $13+8i$.
For the conjugate we must write the vector $(a,-b)$. Therefore as the complex is $13+8i$, we will have: $(13,-8)$ the vector of the conjugate.
$(13,-8)$.
Write the vector associated with the opposite of $13+8i$.
For the opposite of a complex number we must write the vector $(-a,-b)$. In our case it is: $(-13,-8)$.
$(-13,-8)$.