import numpy as np
import matplotlib.pyplot as plt
from IPython.display import display,Math

print('The Pythagorean theorem')
display(Math('c^2 = a^2 + b^2'))

The Pythagorean theorem

$\displaystyle c^2 = a^2 + b^2$

a = 3
b = 4
c = np.sqrt(a**2 + b**2)
print(c)

plt.plot([0,a],[0,0],'k',linewidth=2)
plt.plot([0,0],[0,b],'k')
plt.plot([0,a],[b,0],'k')

plt.plot([.3,.3],[0,.3],'k',linewidth=1)
plt.plot([0,.3],[.3,.3],'k',linewidth=1)

plt.text(a/3,-.45,'a=' + str(a),fontsize=15)
plt.text(.1,b/3,'b=' + str(b),fontsize=15)
plt.text(a/2+.1,b/2,'c=' + str(c),fontsize=15)

plt.axis('square')
axlim = np.max((a,b)) + .5
plt.axis([-.5,axlim,-.5,axlim])
plt.axis('off')
plt.show()

5.0

Exercise

display(Math('\\quad \\quad z = 2 \\quad 3i'))
display(Math('\\quad |z|^2 = 2^2 + 3^2'))
display(Math('tan(k) = 3/2')) # k = radian
plt.plot([0,2],[0,3],'r-',linewidth=2,label='z = 2 3i')
plt.plot([0,2],[0,0],'k-',linewidth=2)
plt.plot([2,2],[0,3],'k-',linewidth=2)
plt.text(.2,.05,'k',fontsize=15)
plt.xlabel('real')
plt.ylabel('imag')
plt.axis('square')
plt.legend()
plt.grid()
plt.show()

$\displaystyle \quad \quad z = 2 \quad 3i$

$\displaystyle \quad |z|^2 = 2^2 + 3^2$

$\displaystyle tan(k) = 3/2$

z = np.complex(3,4)
print(z)

mag1 = np.sqrt(np.real(z)**2 + np.imag(z)**2)
mag2 = np.abs(z)

print(mag1,mag2)

(3+4j)
5.0 5.0

ang1 = np.arctan2(np.imag(z),np.real(z))
ang2 = np.angle(z)

print(ang1,ang2)

0.9272952180016122 0.9272952180016122