TMA4110 Matematikk3
Fall 2015
Norges teknisknaturvitenskapelige
universitet
Institutt for matematiske fag
Øving 2
1 Let z1 = 2 − i and z2 = 1 + i. Use the parallelogram law to construct each of the
following vectors.
a) z1 + z2
b) z1 − z2
c) 2z1 − 3z2
2 Find the following.
1+2i
a) | −2−i
|
b) |(1 + i)(2 − 3i)(4i − 3)|
i(2+i)3
c) | (1−i)2 |
(π+i)100
d) | (π−i)100 |
3 Find the argument of each of the following complex numbers and write each in polar
form.
a) −1/2
b) −3 + 3i
c) −(π)i
√
d) −2 3 − 2i
√
e) (1 − i)(− 3 + i)
√
f ) ( 3 − i)2
√
3i
g) −1+
2+2i
h)
√
− 7(1+i)
√
3+i
4 Find the following.
a) Arg(−6 − 6i)
b) Arg(−π)
c) Arg(10i)
27. august 2015
Side 1 av 2
Øving 2
√
d) Arg( 3 − i)
5 Write each of the given numbers in the form a + bi.
a) e−iπ/4
1+i3π
e
b) e−1+iπ/2
i
c) ee
6 Write each of the given numbers in the polar form reiθ .
a) 1−i
3
b) −8π(1 +
√
3i)
c) (1 + i)6
2π 3
d) (cos 2π
9 + i sin 9 )
e)
2+2i
√
− 3+i
f ) 3e2i
4+i
7 Find all the values of the following.
a) (−16)1/4
b) 11/5
c) i1/4
d) (1 −
√
3i)1/3
e) (i − 1)1/2
2i 1/6
f ) ( 1+i
)
27. august 2015
Side 2 av 2