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z = 4 /(1+ i) Find, in the form a + i b where a, b belong to R, (a) z, (b) z^2. Given that z is a complex root of the quadratic equation x^2 + px + q = 0, where p and q are real integers, (c) find the value of p and the value of q.

a) Need to multiply with conjugate to bring z to form a+ib. => z= z * (1-i)/(1-i) = (4-4i) / 2 = 2-2i b) z^2 = (2-2i)^2 = 4-8i+4 i^2 = 4-8i-4 = 8i since z is root of x^2+px+q=0 then z* (conjugate) is also...
HP
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Find the first derivative of r=sin(theta+sqrt[theta+1]) with respect to theta.

To find the first derivative we must apply the chain rule. Our aim is to find dr/d(theta). We start by bringing the differential of what's inside the sine brackets outside and multiplying it by the different...
TD
Answered by Tutor61926 D. • Maths tutor
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“Outline two criticisms of functionalist based explanations of crime and deviance” [10 marks]

One criticism of the functionalist based explanations of crime and deviance is that functionalists rely on a pattern of crime shown in official crime statistics. However, a lot of crime is never actually rep...
OP
Answered by Olivia P. • Sociology tutor
8847 Views

Describe the series of events from the arrival of an action potential at the pre-synaptic membrane of a cholinergic synapse to the generation of a new action potential at the post synaptic membrane?

An action potential arriving at the pre-synaptic membrane stimulates voltage-gated calcium channels to open and calcium ions diffuse into the neuron through these calcium channels. Influx of calcium causes s...
DZ
Answered by Daniella Z. • Biology tutor
12144 Views

The distance from the Earth to the Sun is 93 million miles. Assume: it takes 365 days for the Earth to travel once around the Sun and the Earth travels in a circle with the Sun at the centre. Work out the average speed of the Earth in miles per hour.

This question is testing your understanding of speed, distance and time and sounds much more complicated than it actually is. For a question like this one, it is best to draw a picture to help you get a bett...
JH
Answered by Jack H. • Maths tutor
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