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Express (3+ i)(1 + 2i) as a complex number in the form a+bi where a and b are real numbers.

One can treat complex multiplication as polynomial multiplication, but remembering i^2 = -1. To perform polynomial multiplication, multiply each term one by one, then add them together. Hence (3+i)(1+2i) ...

Answered by Alvin S. • Maths tutor

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(Using the Quotient Rule) -> Show that the derivative of (cosx)/(sinx) is (-1)/(sinx).

This question is a typical example aimed to test the student's understanding of the quotient rule, a technique which is used very often in calculus problems. Answer: For a function f(x) = cosx/sinx = u/v,...

Answered by Mark H. • Maths tutor

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Find the integral of xe^(-2x) between the limits of 0 and 1 with respect to x.

We can identify xe^(-2x) as a product and hence we will most probably need to use integration by parts.

We then set u = x and v' = x^(-2x). It is important to do it this way round so that when we d...

Answered by Tom B. • Maths tutor

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y=e^(2x) - x^3. Find dy/dx. (please note this is "e to the power of 2x, minus x cubed")

The rules to know are 1) when differentiating e to the power of x... be it 2x or 100x... you bring down the number in front of x, and leave the power as it is. in our case e^(2x) goes to 2e^(2x).

Answered by Toby M. • Maths tutor

7686 Views

How do you find the normal to a curve at a given co-ordinate?

You first find the gradient of the tangent to the curve at this given co-ordinate by differentiating the given equation of the curve, and then, assuming the equation of the curve is in terms of x, r...

Answered by Srabon I. • Maths tutor

4137 Views