For this value of $\theta$, plot the approximate position of $z_{\theta }$ on the Argand diagram.

$\theta =\mathrm{\pi }$.

Find this value of $\theta$.

Hence write down the maximum voltage in the circuit.

$\theta =\frac{3\mathrm{\pi }}{2}$.

An equilateral triangle is to be drawn on the Argand plane with one of the vertices at the point corresponding to $2+5\text{i}$ and all the vertices equidistant from $0$.

Find the points that correspond to the other two vertices. Give your answers in Cartesian form.

Find an expression for $V_T$ in the form $A \cos (Bt+C)$, where $A, B$ and $C$ are real constants.

Find the maximum value of $I_{\text{T}}$.

$\theta =\frac{\mathrm{\pi }}{2}$.

Hence find $\text{Re}\left(w_1+w_2\right)$ in the form $A \cos \left(x-a\right)$, where $A>0$ and $0<a\le \frac{\mathrm{\pi }}{2}$.

Find $w_1+w_2$ in the form ${\text{e}}^{\text{i}x}\left(c+\text{i}d\right)$.

A^–1 = I – A.

A³ = –I.

Show that ${\gamma }^2=\gamma -1$.

Hence find the value of ${\left(1-\gamma \right)}^6$.

Express w² and w³ in modulus-argument form.

$z=1+\text{i}$.

$z=2\text{i}$.

Write down $2+5\text{i}$ in exponential form.

Hence, or otherwise, find the value of $z$ when $w=2-\text{i}$.

Plot the position of $z$ on an Argand Diagram.

Express $z$ in the form $z=a{\text{e}}^{\text{i}b}$, where $a, b\in \mathrm{ℝ}$, giving the exact value of $a$ and the exact value of $b$.

Find the phase shift of $I_{\text{T}}$.