Download Exercises 1

Dr.-Ing.B.Weyh
CB.../Introduction. . .
1
Exercises 1
1
36
compare with (1 − 6 )−1
6
3 √
−1
3
7−2
b) 2 √
−1
( 7 + 2)2
1
c) Area = πr2 with radius r = π 3 − 1
a)
2. Exponential and logarithms:
a) e3 √, ln e3 , log10 e3 , log10(105)
b) eπ 163
c) solve 3x = 17 for x and check the result
(soluton x = lnln17
3 , check by substitution)
3. Trigonometry:
π
,
6π
π
cos π , tan
2
π
b) sin2 + cos2
6
6
c) y = cosh2 x − sinh2 x for x = 32π
4. Complex numbers:
3 + 2i
, check the result by hand calculation
3 π− 2i
b) ei 5 , check the Euler-formula eix = cos x + i sin x by computing both sides of the equation
c) execute the commands exp(pi/2*i) and exp(pi/2i)
explain the difference
a)
CB.../Introduction. . .
Solutions Exercises 1:
1. Arithmetic operations:
a) sin
Dr.-Ing.B.Weyh
>> % 1.Arithmetic operations:
>> 3^6/(3^6-1)
ans =
1.0014
>> (1-1/3^6)^(-1)
ans =
1.0014
>> 2*(sqrt(7)-2)/(sqrt(7+2))^2-1
ans =
-0.8565
>> r=pi^(1/3)-1; Area=pi*r^2
Area =
0.6781
>> % 2. Exponential and logarithms:
>> exp(3), log(exp(3)), log10(exp(3)), log10(1e+5)
ans =
20.0855
ans =
3
ans =
1.3029
ans =
5
>> exp(pi*sqrt(163))
ans =
2.6254e+017
>> x=log(17)/log(3)
x =
2.5789
>> 3^x
ans =
17.0000
2
Dr.-Ing.B.Weyh
>> % 3. Trigonometry:
>> sin(pi/6), cos(pi), tan(pi/2)
ans =
0.5000
ans =
-1
ans =
1.6331e+016
>> sin(pi/6)^2+cos(pi/6)^2
ans =
1
>> x=32*pi; y=cosh(x)^2-sinh(x)^2
y =
0
>> % 4. Complex numbers:
>> (3+2i)/(3-2i)
ans =
0.3846 + 0.9231i
>> exp(i*pi/5)
ans =
0.8090 + 0.5878i
>> x=pi/5; cos(x)+i*sin(x)
ans =
0.8090 + 0.5878i
>> exp(pi/2*i), exp(pi/2i)
ans =
0.0000 + 1.0000i
ans =
0.0000 - 1.0000i
CB.../Introduction. . .
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