Difference between revisions of "MIE 97/98"
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| − | Determine | + | Determine the parameters <math>\alpha</math>, <math>\beta</math>, <math>\gamma</math> and <math>\delta</math> of the complex transformation <math>w=\frac{\alpha z+\beta}{\gamma z+\delta}</math> which takes points <math>z =0;-i;1</math> for <math>w=i;1;0</math>, respectively, as well as <math>z</math> for <math>w=-2-i</math>, where <math>i=\sqrt{-1}</math>. |
===Problem 5=== | ===Problem 5=== | ||
Latest revision as of 20:07, 13 August 2023
Contents
Problem 1
Find the solution of 
with 
.
Problem 2
Solve the following matrix in terms of 
and 
Problem 3
Find the value of 
that satisfies the inequation 
and represent , graphically, the function 
.
Problem 4
Translation needed
Determine the parameters , , 
and 
of the complex transformation 
which takes points 
for 
, respectively, as well as 
for 
, where 
.
Problem 5
Translation needed
Problem 6
Translation needed
Problem 7
Find , and such that the polynomial 
, with 
, is divisible by 
and that the numerical value of the quotient is equal to 
when 
.
Problem 8
A finite sum of integer consecutive numbers, odd, positives or negatives, is equal to 
. Find the terms of this sum.
