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Prove that i^i is real.

Here we are examining the imaginary number ‘i’, defined as the square root (sqrt) of ‘-1’.We begin by using Euler’s identity:e^(iπ)+1=0e^(iπ)=-1Since sqrt(x) is the same as x^(1/2):(e^(iπ))^(...

Answered by Lewis C. • Further Mathematics tutor

7231 Views

How do you calculate the derivative of cos inverse x?
When differentiating cos inverse x, the typical method is to make y equal to cos inverse x.By taking cos of both sides: x = cosy.You can then differentiate with respect to y, obtaining that: (dx/dy) = - s...
WW
Answered by Will W. • Further Mathematics tutor
6514 Views

if y = (e^x)^7 find dy/dx
To solve the the problem we need to recognize what type of differentiation technique we shall be employing

y = (e^x)⁷

the x unction which we are diferen...
GI
Answered by George I. • Further Mathematics tutor
4117 Views

Convert the general complex number z=x+iy to modulus-argument form.
Modulus-argument form implies that we should express z in terms of its straight line distance from the origin and the angle this straight line would make with the x axis. This is expressed as z = r e
BH
Answered by Ben H. • Further Mathematics tutor
10995 Views
The cubic equation 27(z^3) + k(z^2) + 4 = 0 has roots α, β and γ. In the case where β=γ, find the roots of the equation and determine the value of k
This question was worth 8 marks in a 2015 FP2 paper. The first part of this question is tricky, but once we have found the roots it will be easy to plug them in to get the value of k:

Whe...
RG
Answered by Ross G. • Further Mathematics tutor
5374 Views
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Top answers

Prove that i^i is real.

How do you calculate the derivative of cos inverse x?

if y = (e^x)^7 find dy/dx

Convert the general complex number z=x+iy to modulus-argument form.

The cubic equation 27(z^3) + k(z^2) + 4 = 0 has roots α, β and γ. In the case where β=γ, find the roots of the equation and determine the value of k

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