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Find all the cube roots of 1

Let z be a cube root of 1 such that: z^3 = 1 z^3 - 1 = 0 Factorise: (z-1)(z^2 + z + 1) = 0 Then, z=1, the real root, or: z^2 + z + 1 = 0 with z not equal to 1 Use quadratic equation: z = (-1 +- sqrt(1-4))...

OS
4577 Views

Find the four roots of the equation z^4 = + 8(sqrt(3) + i), in the form z = r*e^(i*theta). Draw the roots on an argand diagram.

This is a maths problem, which I believe is best taught by live demonstration and explanation while constantly promtpting the student to suggest further steps if they are able. If they are not, then you s...

AW
8992 Views

How are bacteria genetically modified for human benefit?

First of all, the concept of genetic modification needs to be understood. Proteins are coded for by genes in the DNA of an organism, with each gene coding for a different protein. We utilise the fact that...

DP
Answered by Declan P. Biology tutor
12985 Views

If water is trapped between two planes on a train, and the train decelerates at 4ms^-2. What angle does the surface of the water make with the horizontal?

Draw a diagram of forces on a single particle at surface of water.

Water is stationary in reference to train, thus when including decelerating force, resulting force is zero.

Balance horrizo...

OS
Answered by Oliver S. PAT tutor
2044 Views

Calculate the additional weekly profit the business would make if it produced and sold 5000 novelty mugs every week.

Selling price of novelty mug= £4; Cost of making mug= £2; Distribution cost= £50 for every 100 mugs sold. Therefore, 1) 5000 x £4= £20,000; 2) 5000 x £2= £10,000 3) £20,000- £10,000 = £10,000; 4) 5000/100...

JB
1979 Views

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