-(10%2B4i).jpeg "(3+5i)-(10+4i)")
Subtracting Complex Numbers: (3 + 5i) - (10 + 4i)
In this article, we'll explore how to subtract complex numbers, using the example of (3 + 5i) - (10 + 4i).
Understanding Complex Numbers
Complex numbers are numbers that can be expressed in the form a + bi, where 'a' and 'b' are real numbers, and 'i' is the imaginary unit, defined as the square root of -1.
Subtracting Complex Numbers
To subtract complex numbers, we simply subtract the real and imaginary components separately.
Let's break down the subtraction:
(3 + 5i) - (10 + 4i)
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Distribute the negative sign: 3 + 5i - 10 - 4i
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Combine real terms and imaginary terms: (3 - 10) + (5 - 4)i
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Simplify: -7 + i
Therefore, (3 + 5i) - (10 + 4i) = -7 + i.
Key Points
- Real parts are subtracted: 3 - 10 = -7
- Imaginary parts are subtracted: 5 - 4 = 1
- The result is a complex number in the form a + bi.
By understanding the basic principles of subtracting complex numbers, we can easily solve more complex problems involving these fascinating numbers.