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What Are the Key Steps for Subtracting Complex Numbers?

Subtracting complex numbers might seem tricky, but it’s actually easy once you know the steps. Here’s a simple way to do it:

  1. Know the Structure: A complex number looks like this: a+bia + bi. Here, aa is the real part, and bb is the imaginary part. For example, if you have two complex numbers, z1=a+biz_1 = a + bi and z2=c+diz_2 = c + di, then aa, bb, cc, and dd are all real numbers.

  2. Set Up for Subtraction: To subtract these complex numbers, write it like this: z1z2=(a+bi)(c+di)z_1 - z_2 = (a + bi) - (c + di)

  3. Apply the Negative Sign: This is a common mistake, but it’s simple! Just take away both parts of the second complex number: z1z2=a+bicdiz_1 - z_2 = a + bi - c - di

  4. Combine Like Terms: Now, put together the real parts and the imaginary parts: z1z2=(ac)+(bd)iz_1 - z_2 = (a - c) + (b - d)i This shows your new result clearly, with (ac)(a - c) as the new real part and (bd)(b - d) as the new imaginary part.

  5. Write Your Final Answer: You've done it! Your answer is a new complex number, written as (ac)+(bd)i(a - c) + (b - d)i.

  6. Practice to Improve: Like any math skill, the more you practice subtracting complex numbers, the better you’ll get. Try working on a few examples to feel more comfortable.

In short, remember to know the structure of complex numbers, set them up right, apply the negative sign, and combine like terms. Soon enough, subtracting complex numbers will feel easy!

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What Are the Key Steps for Subtracting Complex Numbers?

Subtracting complex numbers might seem tricky, but it’s actually easy once you know the steps. Here’s a simple way to do it:

  1. Know the Structure: A complex number looks like this: a+bia + bi. Here, aa is the real part, and bb is the imaginary part. For example, if you have two complex numbers, z1=a+biz_1 = a + bi and z2=c+diz_2 = c + di, then aa, bb, cc, and dd are all real numbers.

  2. Set Up for Subtraction: To subtract these complex numbers, write it like this: z1z2=(a+bi)(c+di)z_1 - z_2 = (a + bi) - (c + di)

  3. Apply the Negative Sign: This is a common mistake, but it’s simple! Just take away both parts of the second complex number: z1z2=a+bicdiz_1 - z_2 = a + bi - c - di

  4. Combine Like Terms: Now, put together the real parts and the imaginary parts: z1z2=(ac)+(bd)iz_1 - z_2 = (a - c) + (b - d)i This shows your new result clearly, with (ac)(a - c) as the new real part and (bd)(b - d) as the new imaginary part.

  5. Write Your Final Answer: You've done it! Your answer is a new complex number, written as (ac)+(bd)i(a - c) + (b - d)i.

  6. Practice to Improve: Like any math skill, the more you practice subtracting complex numbers, the better you’ll get. Try working on a few examples to feel more comfortable.

In short, remember to know the structure of complex numbers, set them up right, apply the negative sign, and combine like terms. Soon enough, subtracting complex numbers will feel easy!

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