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Why is the argument of a+bi equal to arctan(b/a)?

Think about the point a+bi on the complex plane. Specifically, a is how far along the x (real) axis, and b is how far up the y (imaginary) axis the point is. If you draw a line connecting the origin and t...

Answered by Martin S. • Further Mathematics tutor

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How to plan a A Level History source question?

Extract A Argument Claims: Judgement in response: Factual Information to the validity (or not) of claims: Summary of Paragraph:

Answered by Ines D. • History tutor

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Please use the VSEPR theory to predict the shape of NH3 and the approximate bond angles

The student should draw the lewis structure - this should be worked through using the whiteboard 2. From the lewis structure it can be identified that NH3 has 3 bonds and one lone pair of electrons ...

Answered by Alisha G. • Chemistry tutor

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For the equilibrium reaction PCl5(g) (equilibrium arrow)-> PCl3(g) + Cl2(g) explain the effect of increasing the concentration of Chlorine gas using the equilibrium constant.

Kc=[Cl2(g)][PCl3(g)]/[PCl5(g)] for this reaction. The rate constant is not affected by changes in concentration and hence an increase in the concentration of Chlorine causes an increase in the concentrati...

Answered by James H. • Chemistry tutor

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A general function f(x) has the property f(-x)=-f(x). State a trigonometric function with this property and explain using the Maclaurin series expansion for this function why this property holds. Write down the integral in the limits -q to q of f(x) wrt x

Note that this property is the definition of an odd function, or draw a sketch of what this looks like in general about the horizontal axis. E.g. f(x)=sin(x) which has the expansion f(x)=x-((x^3)/3!)+((x^...

Answered by James H. • Maths tutor

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