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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
15512 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
9034 Views

Lengths of two sides of the triangle and the angle between them are known. Find the length of the third side and the area of the triangle.

We don't know what type of a triangle we're considering here. Therefore the universal and quickest solution to the first problem is use of the cosine rule, which states that for a triangle with sides a,b and...
SK
8039 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
10391 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
4036 Views