Arithmetic in Python — From Basics to Complex Numbers
Learn operators, precedence, parentheses, complex numbers, and practical examples. Try assignments and reveal answers interactively.
1) Complex Numbers in Python
z1 = 3 + 4j
z2 = 1 - 2j
print(z1 + z2) # (4+2j)
print(z1 * z2) # (11-2j)
print(abs(z1)) # 5.0
2) Parentheses and Precedence
result1 = 10 + 5 * 2 ** 2
print(result1) # 30
result2 = (10 + 5) * (2 ** 2)
print(result2) # 60
3) Square Roots: Two Variations
Python allows you to compute square roots either with math.sqrt() or by raising a number to the power of 0.5.
import math
print(math.sqrt(16)) # 4.0 (using math.sqrt)
print(16 ** 0.5) # 4.0 (using exponentiation)
You can extend this idea for other roots:
print(27 ** (1/3)) # 3.0 (cube root)
print(32 ** 0.2) # 2.0 (5th root)
4) Practical Examples
a) Area of Triangle
a, b, c = 5, 6, 7
s = (a + b + c) / 2
area1 = (s*(s-a)*(s-b)*(s-c)) ** 0.5 # using **0.5
area2 = math.sqrt(s*(s-a)*(s-b)*(s-c)) # using math.sqrt
print(area1, area2)
b) Quadratic Equations
import cmath
a, b, c = 1, 2, 5
d = (b**2) - (4*a*c)
r1 = (-b + cmath.sqrt(d)) / (2*a)
r2 = (-b - cmath.sqrt(d)) / (2*a)
print(r1, r2)
5) Assignments (Click to Show Answer)
Q1: Calculate perimeter and area of a rectangle (length=12, breadth=8).
length, breadth = 12, 8
perimeter = 2*(length + breadth)
area = length * breadth
print(perimeter, area) # 40, 96
Q2: Solve quadratic equation x² + 3x + 2 = 0.
import cmath
a, b, c = 1, 3, 2
d = (b**2) - (4*a*c)
r1 = (-b + cmath.sqrt(d))/(2*a)
r2 = (-b - cmath.sqrt(d))/(2*a)
print(r1, r2) # (-1+0j), (-2+0j)
Q3: Find the Simple Interest for P=2000, R=7%, T=3 years.
P, R, T = 2000, 7, 3
SI = (P * R * T)/100
print(SI) # 420
Q4 (Multi-Step): Given the area of a circle (314), find the radius, then use it to compute the circumference and diameter. Try both **0.5 and math.sqrt() for the square root.
import math
area = 314
# radius with **0.5
radius1 = (area / math.pi) ** 0.5
# radius with math.sqrt
radius2 = math.sqrt(area / math.pi)
circumference = 2 * math.pi * radius1
diameter = 2 * radius1
print(radius1, radius2, circumference, diameter)
# ~10.0, ~10.0, ~62.83, ~20.0
Q5 (Multi-Step): A savings account earns compound interest at 8% per year. If you invest 2000 for 3 years, first compute the total amount, then subtract principal to find interest.
P, R, T = 2000, 8, 3
A = P * ((1+R/100)**T)
CI = A - P
print(A, CI)
# 2519.42, 519.42
Q6 (Multi-Step): Given speed=60 km/h and time=2.5 h, calculate distance. Then convert distance to meters.
speed, time = 60, 2.5
distance_km = speed * time
distance_m = distance_km * 1000
print(distance_km, distance_m) # 150.0, 150000.0
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