{
"metadata": {
"name": "",
"signature": "sha256:e4e0b2e74a0b30b96b3a586de7b740bbefabf9c41230a1638409bfb7b309d066"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Chapter 23: Revision of complex numbers
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 1, page no. 418
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Determine ZT\n",
"from __future__ import division\n",
"import math\n",
"import cmath\n",
"#initializing the variables:\n",
"Z1 = 5 - 3j;\n",
"Z2 = 4 + 7j;\n",
"Z3 = 3.9 - 6.7j;\n",
"\n",
" #calculation:\n",
"ZT = (Z1*Z2/(Z1 + Z2))+ Z3\n",
"y = ZT.imag\n",
"x = ZT.real\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n ZT is \",round(x,2),\" + (\",round(y,2),\")i\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" ZT is 8.65 + ( -6.26 )i"
]
}
],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 2, page no. 418
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#determine in cartesian form correct to three decimal places:\n",
"#(a)1/Z1 (b)1/Z2 (c) 1/Z1 * 1/Z2 (d) 1/(1/Z1 + 1/Z2)\n",
"from __future__ import division\n",
"import math\n",
"import cmath\n",
"#initializing the variables:\n",
"Z1 = 3 + 4j;\n",
"Z2 = 2 - 5j;\n",
"\n",
"#calculation:\n",
"za = 1/Z1\n",
"zb = 1/Z2\n",
"zc = za + zb\n",
"zd = 1/zc\n",
"zax = za.real\n",
"zay = za.imag\n",
"zbx = zb.real\n",
"zby = zb.imag\n",
"zcx = zc.real\n",
"zcy = zc.imag\n",
"zdx = zd.real\n",
"zdy = zd.imag\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)1/Z1 is \",round( zax,2),\" + (\",round(zay,2),\")i\"\n",
"print \"\\n (b)1/Z2 is \",round( zbx,2),\" + (\",round(zby,2),\")i\"\n",
"print \"\\n (c)1/Z1 + 1/Z2 is \",round( zcx,2),\" + (\",round(zcy,2),\")i\"\n",
"print \"\\n (d)1/(1/Z1 + 1/Z2) is \",round( zdx,2),\" + (\",round(zdy,2),\")i\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)1/Z1 is 0.12 + ( -0.16 )i\n",
"\n",
" (b)1/Z2 is 0.07 + ( 0.17 )i\n",
"\n",
" (c)1/Z1 + 1/Z2 is 0.19 + ( 0.01 )i\n",
"\n",
" (d)1/(1/Z1 + 1/Z2) is 5.27 + ( -0.35 )i"
]
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 3, page no. 419
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#find a, b, x and y?\n",
"from __future__ import division\n",
"import math\n",
"import cmath\n",
"#initializing the variables:\n",
"Z1 = 9 - 2j;\n",
"Z2 = 2 + 1j;\n",
"Z3 = -2 + 1j;\n",
"Z4 = 5 + 2j;\n",
"\n",
"#calculation:\n",
"za = Z1/3\n",
"zb = Z2*Z3\n",
"zca = (2*Z4.real + Z4.imag)/-1\n",
"zcb = Z4.real - zca\n",
"zaa = za.real\n",
"zab = za.imag\n",
"zbx = zb.real\n",
"zby = zb.imag\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)a and b are \", zaa,\" and \",round(zab,2),\" resp.\"\n",
"print \"\\n (b)x and y are \", zbx,\" and \",zby,\" resp.\"\n",
"print \"\\n (c)a and b are \", zca,\" and \",zcb,\" resp.\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)a and b are 3.0 and -0.67 resp.\n",
"\n",
" (b)x and y are -5.0 and 0.0 resp.\n",
"\n",
" (c)a and b are -12.0 and 17.0 resp."
]
}
],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 5, page no. 422
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Convert 5/_132\u00b0 into a + jb form correct to four significant figures.\n",
"from __future__ import division\n",
"import math\n",
"import cmath\n",
"#initializing the variables:\n",
"r = 5;# magnitude\n",
"theta = -132;# in degree\n",
"\n",
"#calculation:\n",
"x = r*math.sin(theta*math.pi/180)\n",
"y = r*math.cos(theta*math.pi/180)\n",
"z = x + y*1j\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n Z is \",round(x,2),\" + (\",round(y,2),\")i\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" Z is -3.72 + ( -3.35 )i"
]
}
],
"prompt_number": 6
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 6, page no. 422
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Determine in polar form the total impedance ZT given that ZT = Z1Z2/\u0007(Z1 + Z2\b)\n",
"from __future__ import division\n",
"import math\n",
"import cmath\n",
"#initializing the variables:\n",
"r1 = 4.76;# magnitude\n",
"theta1 = 35;# in degree\n",
"r2 = 7.36;# magnitude\n",
"theta2 = -48;# in degree\n",
"\n",
"#calculation:\n",
"x1 = r1*cmath.cos(theta1*math.pi/180)\n",
"y1 = r1*cmath.sin(theta1*math.pi/180)\n",
"z1 = x1 + y1*1j\n",
"x2 = r2*cmath.cos(theta2*math.pi/180)\n",
"y2 = r2*cmath.sin(theta2*math.pi/180)\n",
"z2 = x2 + y2*1j\n",
"z3 = z1*z2/(z1 + z2)\n",
"x3 = z3.real\n",
"y3 = z3.imag\n",
"r3 = (x3**2 + y3**2)**0.5\n",
"theta3 = cmath.phase(complex(x3,y3))*180/math.pi\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n ZT is (\",round( r3,2),\",round(/_\",round(theta3,2),\"deg)\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" ZT is ( 3.79 ,round(/_ 4.25 deg)"
]
}
],
"prompt_number": 7
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 7, page no. 423
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Determine \u0007\u0003(2 +j3\b)^5 in polar and in cartesian form.\n",
"from __future__ import division\n",
"import math\n",
"import cmath\n",
"#initializing the variables:\n",
"z = -2 + 3j;\n",
"\n",
"#calculation:\n",
"zc = z**5\n",
"x = zc.real\n",
"y = zc.imag\n",
"r = (x**2 + y**2)**0.5\n",
"theta = cmath.phase(complex(x,y))*180/math.pi\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n Z is \",round( x,2),\" + (\",round(y,2),\")i\"\n",
"print \"\\n ZT is (\",round( r,2),\"round/_\",round(theta,2),\"deg)\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" Z is -122.0 + ( -597.0 )i\n",
"\n",
" ZT is ( 609.34 round/_ -101.55 deg)"
]
}
],
"prompt_number": 8
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 8, page no. 423
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Determine the two square roots of the complex number \u0007(12 + j5)\b in cartesian and polar form\n",
"from __future__ import division\n",
"import math\n",
"import cmath\n",
"#initializing the variables:\n",
"z = 12 + 5j;\n",
"\n",
"#calculation:\n",
"x = z.real\n",
"y = z.imag\n",
"r = (x**2 + y**2)**0.5\n",
"theta1 = cmath.atan(y/x)*180/math.pi\n",
"'''\n",
"if ((x<0)&(y<0))\n",
" theta1 = theta1 -180;\n",
"elif ((x<0)&(y>0))\n",
" theta1 = theta1 +180;\n",
"'''\n",
"theta2 = theta1 + 360\n",
"rtheta1 = theta1/2\n",
"rtheta2 = theta2/2\n",
"'''\n",
"if (rtheta2 > 180)\n",
" rtheta2 = rtheta2 -360;\n",
"elif ((x<0)&(y>0))\n",
" rtheta2 = rtheta2 +360;\n",
"'''\n",
"rr = r**0.5\n",
"x1 = rr*cmath.cos(rtheta1*math.pi/180)\n",
"y1 = rr*cmath.sin(rtheta1*math.pi/180)\n",
"z1 = x1 + y1*1j\n",
"\n",
"x2 = rr*cmath.cos(rtheta2*math.pi/180)\n",
"y2 = rr*cmath.sin(rtheta2*math.pi/180)\n",
"z2 = x2 + y2*1j\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n two roots are (\",round(z1.real,2),\" + (\",round(z1.imag,2),\")i) \"\n",
"print \" and (\",round(z2.real,2),\" + (\",round(z2.imag,2),\")i)\"\n",
"print \"\\n two roots are (\",round( rr,2),\"/_\",round((cmath.phase(complex(z1.real,z1.imag)))*180/math.pi,2),\"deg) \"\n",
"print \" and (\",round( rr,2),\"/_\",round((cmath.phase(complex(z2.real,z2.imag)))*180/math.pi,2),\"deg)\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" two roots are ( 3.54 + ( 0.71 )i) \n",
" and ( -3.54 + ( -0.71 )i)\n",
"\n",
" two roots are ( 3.61 /_ 11.31 deg) \n",
" and ( 3.61 /_ -168.69 deg)\n"
]
}
],
"prompt_number": 1
}
],
"metadata": {}
}
]
}