a. Work out the product of the following complex numbers; note that a is a constant:...

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a. Work out the product of the following complex numbers; note that a is a constant: i. (96i) (112i) ii. (3a-i) (-2+ 14ai) (2 marks for each part) b. When an alternating current is sent through a wire coil, the current flow is impeded by it in the same way that a resistor resists or impedes the flow of electrical current through it. It is said to have an impedance - just as a resistor has a resistance. However, because the electrical signal also experiences a phase change, it is usual to refer to it as a complex number, Z. We can write the impedance as: Z = 2infL where fis the frequency of the current passed through the coil, L is the inductance of the coil (in units of henry, H) and i is the complex number such that ² = -1. If the current passing through the coil has a frequency of 60 Hz (i.e. f = 60) and a magnitude of 0.5 A, then we can write it as: I = 0.5 cos (2 x 60nt) +0.5i sin (2 x 60πt) where t is time. Assume that Ohm's Law applies to coils (or inductors), in other words, the voltage V across the coil is given by V = IZ. Calculate the impedance of this coil and the voltage across it as a complex number when L = 5 x 10-³ H and t = 0.001 s. Give your answers to one decimal place. a. Work out the product of the following complex numbers; note that a is a constant: i. (96i) (112i) ii. (3a-i) (-2+ 14ai) (2 marks for each part) b. When an alternating current is sent through a wire coil, the current flow is impeded by it in the same way that a resistor resists or impedes the flow of electrical current through it. It is said to have an impedance - just as a resistor has a resistance. However, because the electrical signal also experiences a phase change, it is usual to refer to it as a complex number, Z. We can write the impedance as: Z = 2infL where fis the frequency of the current passed through the coil, L is the inductance of the coil (in units of henry, H) and i is the complex number such that ² = -1. If the current passing through the coil has a frequency of 60 Hz (i.e. f = 60) and a magnitude of 0.5 A, then we can write it as: I = 0.5 cos (2 x 60nt) +0.5i sin (2 x 60πt) where t is time. Assume that Ohm's Law applies to coils (or inductors), in other words, the voltage V across the coil is given by V = IZ. Calculate the impedance of this coil and the voltage across it as a complex number when L = 5 x 10-³ H and t = 0.001 s. Give your answers to one decimal place.