1.1



In [17]:

    
%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
z1 = 1 + 2j
z2 = 2 + 1j

def show_graph(imag_items, labels=None):
    coords = tuple(map(lambda x: (x.real, x.imag), imag_items))
    arrows = np.array(list(map(lambda x: (0,0,x[0],x[1]), coords)))
    X,Y,U,V = zip(*arrows)
    plt.figure(figsize=(8, 8))
    ax = plt.gca()
    ax.set_aspect('equal', adjustable='box')
    ax.quiver(X,Y,U,V,angles='xy',scale_units='xy',scale=1)
    
    max_number = 0
    for c in coords:
        max_number =max(max_number, max(map(abs, c)))
    max_number += 1
    ax.set_xlim([-max_number,max_number])
    ax.set_ylim([-max_number,max_number])

    for val in ax.spines.values():
        val.set_position('center')
        
    if labels is not None:
        for coord, label in zip(coords, labels):
            plt.annotate(label, xy=coord)

    plt.draw()
    plt.show()

show_graph((z1, z2), ('z1', 'z2'))

1.2



In [18]:

    
import cmath as cm
import math as m
z1 = 1 + 2j
z2 = 2 + 1j
print('abs z1:', abs(z1), '\nphase z1', (cm.phase(z1)/m.pi)*180)
print('abs z2:', abs(z2), '\nphase z2', (cm.phase(z2)/m.pi)*180)









    



abs z1: 2.23606797749979 
phase z1 63.43494882292201
abs z2: 2.23606797749979 
phase z2 26.565051177077986

1.3



In [19]:

    
show_graph((z1, z2, 3 + 3j), ('z1', 'z2', 'z1 + z2'))
show_graph((z1, z2, -1 + 1j), ('z1', 'z2', 'z1 - z2'))

1.4



In [20]:

    
def ctimes(z1, z2):
    a = z1.real
    b = z1.imag
    c = z2.real
    d = z2.imag
    return (a*c - b*d) + (a*d + b*c)*1j
show_graph((z1, z2, ctimes(z1, z2)), ('z1', 'z2', 'z1 * z2'))

def cdiv(z1, z2):
    a = z1.real
    b = z1.imag
    c = z2.real
    d = z2.imag
    return (a*c + b*d)/(c**2 + d**2) + ((b*c - a*d)/(c**2 + d**2))*1j
show_graph((z1, z2, cdiv(z1, z2)), ('z1', 'z2', 'z1 / z2'))

1.5



In [21]:

    
z1d = 1/z1
z2d = 1/z2
print(z1d, z2d)
show_graph((z1d, z2d, ctimes(z1d, z2d)), ('1/z1', '1/z2', '1/z1 * 1/z2'))
show_graph((z1d, z2d, cdiv(z1d, z2d)), ('1/z1', '1/z2', '(1/z1) / (1/z2)'))









    



(0.2-0.4j) (0.4-0.2j)

complex getal	reële deel	imaginaire deel	absolute waarde	hoek in graden
$z_1 = 1 + 2j$	1	2	2.24	63.4
$z_2 = 2 + j$	2	1	2.24	26.6
$z_1 + z_2$	3	3	$\sqrt{2*3^2} = 4.24$	45
$z_1 - z_2$	-1	1	$\sqrt{2}$	45
$z_1 \times z_2$	0	5.02	$2.24 * 2.24 = 5.02$	90
$z_1 / z_2$	$4/5$	$3/5$	$2.24/2.24 = 1$	$63.4 - 26.6 = 36.8$
$1/z_1$	$1/5$	$-2/5$	$1/2.24 = 0.45$	-63.4
$1/z_2$	$2/5$	$-1/5$	0.45	-26.6

2

complex getal	reële deel	imaginaire deel	absolute waarde	hoek in graden
$z_1 = 1 + 2j$	1	1	$\sqrt{2}$	45
$z_2 = 2 + j$	-1	1	$\sqrt{2}$	135
$z_1 + z_2$	0	2	2	90
$z_1 - z_2$	2	0	2	0
$z_1 \times z_2$	-2	0	2	180
$z_1 / z_2$	0	-1	1	-90
$1/z_1$	$0.5$	$-0.5$	$1/\sqrt{2}$	-45
$1/z_2$	$-0.5$	$-0.5$	$1/\sqrt{2}$	-135

3

4.1

z1: abs = $\sqrt{2}$, hoek=45

z2: abs = 0.781, hoek=50

4.2



In [22]:

    
z1 = m.sqrt(2)*m.e**0.7854j
z2 = 0.781*m.e**0.876j

print('real:', z1.real, ', img:', z1.imag)
print('real:', z2.real, ', img:', z2.imag)









    



real: 0.9999981633957618 , img: 1.0000018366008652
real: 0.5000188445409669 , img: 0.5999517939834137

4.3

$z1*z2$: abs=$0.781\sqrt{2}$, hoek=95

$z1/z2$: abs=$\sqrt{2}/0.781$, hoek=5

4.4



In [23]:

    
show_graph((z1, z2, z1*z2, z1/z2), ('z1', 'z2', 'z1 * z2', 'z1/z2'))