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Find the square root of i

When dealing with powers of complex numbers, always start by putting the quantity into exponential form. i has a magnitude of 1 and an argument of π/2 . Using Euler's formula, i = exp(iπ/2) Now the expressio...
JL
15465 Views

Find arsinh(x) in terms of x

let y=arsinh(x)x=sinh(y)=(e y - e -y )/22x=e y - e -y 2x*e y =e y -1 (multiply bye y )0=(e y ) 2 -2xe y -1This is a quadratic in e y with coefficients: a=1,b=-2x,c=-1Usinng the quadratic formula (and simplif...
JB
8996 Views

write 2-2i in its modulus argument form

firsly sketch out the 2-2i on an argand diagrm and draw a line from (0,0) to (2,-2). With the shortest distance Mark the angle theta from the positive x-axis to the line to see whether the argument is positi...
ZS
10371 Views

Find the inverse of the general 2x2 matrix A= ([a, b],[c, d]) when does this inverse exist?

This is a typical further maths question, doing it correctly is a matter of carrying out a two-step process. Start by finding the determinant of the matrix, det(A)=ad-bc Then swap the entries a d and negate ...
LR
4013 Views

The curve C has polar equation 'r = 3a(1 + cos(x)). The tangent to C at point A is parallel to the initial line. Find the co-ordinates of A. 0<x<pi

Tangent is parallel, therefore (dy/dx)=0. Find y: y = r sin(x) = 3a(1 + cos(x))(sin(x)) Differentiate y with respect to x dy/dx = 3a[(2cos(x) - 1)(cos(x) + 1)] = 0 Solve equation 2cos(x)- 1 = 0 cos(x) = 1/2 ...
SS
7901 Views