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How do I find the square root of a complex number?

Say you want to find the square root of the complex number 3+2i.
We can assume that the answer we want will be in the form a+bi.
It follows then, that you can also write 3+2i as (a+bi)²

Answered by Dan C. • Further Mathematics tutor

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A curve has equation: y = x^3 - 3x^2 + 5. Show that the curve has a minimum point when x = 2.

A minimum point will have a gradient of 0 (although so will a maximum point or a point of inflection). dy/dx = 3x²-6x. We can substitute x = 2 into this equation to give 0 (alternatively solve ...

Answered by Tom C. • Further Mathematics tutor

7912 Views

Given y=arctan(3e^2x). Show dy/dx= 3/(5cosh(2x) + 4sinh(2x))

As we cannot immediately differentiate inverse tan we take tan of both sides giving us tan(y)=3e^2x.We then differentiate with respect to x, however this must be done using implicit differentia...

Answered by Matt S. • Further Mathematics tutor

5299 Views

A block of mass 50kg resting on a rough surface with a coefficient of friction equal to 1/3. Find the maximum angle at which the surface can be inclined to the horizontal without the block slipping. Give your answer to 3 significant figures

Break the solution down into small logical steps, outlining thought process in each one to make it clear to the examiner what it is you are try to do. Emphasise the importance of a clear and neat layout o...

Answered by Seth F. • Further Mathematics tutor

3294 Views

How do I apply mathematical induction to answer questions

If you are familiar with induction but unsure how to answer the types of questions that require it, a structure can be useful.
Even when confident, it will help an examiner to see where to award you ...

Answered by Oliver M. • Further Mathematics tutor

2166 Views