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=== | ||
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===Problem 8=== | ===Problem 8=== | ||
− | A | + | A finite sum of integer consecutive numbers, odd, positives or negatives, is equal to <math>7^3</math>. Find the terms of this sum. |
Latest revision as of 21:07, 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.