### Engagement Talks

Here you will find three engagement talks (videos of approx. 10 mins) that cover very different areas of maths and physics.

If you would like to ask any of the speakers a question or even just comment on their talk then please type this in to the box below their talk and we will send it directly to them. Their responses will be uploaded here in early August and we will email you to let you know.

Click the talk titles below to start watching.

### The Skeleton of Our Universe

### Your questions answered by Cora in 2020.

#### "Do you think we will we ever be able to develop telescopes powerful enough to record videos that are practically in real-time?“ (anonymous)

#### "If the galaxy continued to expand, would it ever expand so extensively that it collided with another galaxy? If so, what happens then?“ (anonymous)

#### "Thank you for giving up your time to do that talk - it was so interesting! I was curious to ask about the cosmic web. I'd like to know a bit more about what it is that causes some galaxies to move away from us and some to move towards us." (Cora A)

#### "Also, do we have records of other planets experiencing this kind of shift with other stars.etc and if not, do we aspire to investigate this deeper in the future?" (Cora A)

### The Reality of Imaginary Numbers

### Your questions answered by Matina in 2020.

#### ”Please could you explain in more detail how complex numbers are used in circuits?” (anonymous)

An AC circuit can be described by the voltage \(V\) (Volts), the current \(I\) (Amps) and the impedance \(Z\) (Ohms). Voltage measures the energy that a charge gets when it moves between two points, an electric current is the rate of flow of charge past a point and impedance measures the opposition of an electrical circuit to the flow of electricity when voltage is applied. We represent the impedance as a complex number and Ohm’s Law becomes \[V = IZ.\]

For example, if the circuit has a current \(I = 4 + 2i\) and an impedance \(Z = 1 - i\), then \[\begin{align}V & = (4 + 2i)(1 - i) \\ & = 4 - 4i + 2i - 2i^2 \\ & = 4 - 4i + 2i + 2 \\ & = 6 − 2i.\end{align}\]

Further notes: In a series circuit, the impedance is the sum of the impedances for the individual circuit components. In a parallel circuit, there are several paths through which the current can flow. If we have two impedances \(Z_1\) and \(Z_2\) connected in parallel, then the total impedance is given by \[Z_t = \frac{Z_1Z_2}{Z_1 + Z_2}.\]

We also note that complex numbers are used to analyse DC circuits.