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.

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

Describe these two transformations and give the order in which they are applied.

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.

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

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 $I_{\text{T}}$.