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Write the complex number Z=1/2+sqrt(3)/2j both as a function involving cos & sin, and as a function involving an exponential.

|Z| = sqrt(1/2^2 + (sqrt(3)/2)^2) = 1 arg(Z) = arctan((sqrt(3)/2)/(1/2)) = pi/3 Z = cos(pi/3) + jsin(pi/3) Z = e^j(pi/3) Apologies for the use of sqrt(), I have no way yet of using the symbol on my laptop...

Answered by Sol R. • Maths tutor

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Let f(x) = 5x^4 + 6x^3 + 3, find dy/dx at x = 3

First we must differentiate the equation with respect to x. To differentiate you must multiply the coefficient (number in front) by the power of x, then subtract 1 from the power. So here we find dy/dx = ...

Answered by Francesca K. • Maths tutor

3422 Views

Rearrange the following making a the subject: (a+2)/5 = 3a+b

(a+2)/5 = 3a+b ...first, we need to multiply both sides by 5

a + 2 = 5 (3a + b) ....to be able substract 3a from the right side we need to remove the bracket. We multiply the bracket by 5.

Answered by Katerina R. • Maths tutor

3360 Views

Expand the following: (4x+7)(7x-2)

Using the FOIL (Firsts, Outsides, Insides, Lasts) mnemonic, you can expand these two brackets. F: 4x x 7x = 28x^2 O: 4x x -2 = -8x I: 7 x 7x = 49x L: 7 x -2 = -14 Therefore the expansion as a whole is: 28...

Answered by Gem P. • Maths tutor

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