Adding and Subtracting Complex Numbers Examples
Question 1. Find the sum of the two complex numbers z = 3 + 5i and w = 6 – 2i.
Solution:
Since the given complex numbers have real and imaginary parts, we can combine them to find the net sum of both the complex numbers.
z + w = (3 + 5i) + (6 – 2i) = (3 + 6) + i (5 – 2)
z + w = 9 + 3i
Thus, the sum of the complex numbers is equal to 9 + 3i.
Question 2. Subtract the complex numbers z = 2 – 3i and w = -4 + 2i.
Solution:
Since, we can combine the real and imaginary terms of the complex numbers and apply our operations, we can write
z – w = (2 – 3i) – (-4 + 2i) = (2 -(-4)) + i (-3 -2)
z – w = 6 – 5i
Thus, the result is 6 – 5i.
Question 3. Given the complex numbers z1 = 3 + 2i, z2 = 5 – 3i and z3 = 1 + 2i, find the value of z1 + z2 – z3.
Solution:
Given the three complex numbers z1 = 3 + 2i, z2 = 5 – 3i and z3 = 1 + 2i, we can apply associative property of complex numbers to find the result.
Thus, we can write,
z1 + z2 – z3 = (z1 + z2) – z3 = ((3 + 2i) + (5 – 3i)) – (1 + 2i)
z1 + z2 – z3 = (8 – i) – (1 + 2i) = (8 – 1) + i(-1 – 2)
z1 + z2 – z3 = 7 – 3i
So, the answer is 7 – 3i.
Question 4. Given the two complex numbers z and v, where z = 6 + 9i. If the sum of the two complex numbers is twice the value when v is subtracted from z, find the value of v.
Solution:
Given, the complex number z = 5 + 2i.
According to the question,
z + v = 2 (z – v)
z + v = 2z – 2v
3v = z
v = z/3
Putting the value of z = 6 + 9i, we get
v = (6 + 9i)/3 = 6/3 + i (9/3) = 2 + 3i
v = 2 + 3i
Adding and Subtracting Complex Numbers
Adding and Subtracting Complex Numbers: A complex number comprises a real number and an imaginary number. It is usually represented in the form of z = a + ib, where a is the real part and b is the imaginary part. Here, i represents an imaginary unit number, whose value is equal to √-1. Thus, i = √-1.
This article provides the steps to add or subtract complex numbers, with solved examples and properties of addition or subtraction of complex numbers.
Table of Content
- Addition of Complex Numbers
- Subtraction of Complex Numbers
- How to Add or Subtract Complex Numbers?
- Properties of Adding or Subtracting Complex Numbers
- Adding and Subtracting Complex Numbers Examples
- Adding and Subtracting Complex Numbers Worksheet