In mathematics, equality of complex numbers refers to the comparison of two complex numbers to determine if they are equal or not. A complex number is a number of the form a + bi, where a and b are real numbers and i is the imaginary unit (√-1).
To understand equality of complex numbers, one must have knowledge of the following concepts:
The formula for equality of complex numbers is straightforward. Two complex numbers a + bi and c + di are equal if and only if their real parts (a and c) are equal and their imaginary parts (b and d) are equal. Mathematically, this can be expressed as:
a + bi = c + di if and only if a = c and b = d
To apply the formula for equality of complex numbers, we compare the real parts and imaginary parts separately. If both the real and imaginary parts of two complex numbers are equal, then the complex numbers are considered equal.
The symbol used to represent equality of complex numbers is the equal sign (=), just like in other mathematical equations.
There are a few methods to determine the equality of complex numbers:
Are the complex numbers (3 + 2i) and (3 + 2i) equal? Solution: Yes, the real parts (3) and imaginary parts (2) of both complex numbers are equal, so they are equal.
Determine if the complex numbers (4 + 5i) and (5 + 4i) are equal. Solution: No, the real parts (4 and 5) and imaginary parts (5 and 4) are not equal, so the complex numbers are not equal.
Q: What is equality of complex numbers? A: Equality of complex numbers refers to comparing two complex numbers to determine if they are equal or not.
Q: How do you determine if two complex numbers are equal? A: To determine if two complex numbers are equal, compare their real parts and imaginary parts separately. If both parts are equal, the complex numbers are considered equal.
Q: What is the formula for equality of complex numbers? A: The formula for equality of complex numbers states that two complex numbers are equal if and only if their real parts are equal and their imaginary parts are equal.