When you multiply complex numbers, it's a lot like multiplying regular polynomials. Let’s make it simple:
1. Identify the Numbers: Imagine you have two complex numbers: (a + bi) and (c + di).
2. Use the Distributive Property: You will multiply each part of the first complex number with each part of the second one. Here’s what it looks like:
[ (a + bi)(c + di) = ac + adi + bci + bdi^2 ]
3. Simplify the Expression: Remember that (i^2 = -1). So, we can replace (i^2) with (-1):
[ = ac + adi + bci - bd ]
Now, let’s put the real and imaginary parts together:
[ (ac - bd) + (ad + bc)i ]
By paying attention to the real (regular numbers) and imaginary (numbers with (i)) parts, you’ll correctly multiply complex numbers using the distributive property!
When you multiply complex numbers, it's a lot like multiplying regular polynomials. Let’s make it simple:
1. Identify the Numbers: Imagine you have two complex numbers: (a + bi) and (c + di).
2. Use the Distributive Property: You will multiply each part of the first complex number with each part of the second one. Here’s what it looks like:
[ (a + bi)(c + di) = ac + adi + bci + bdi^2 ]
3. Simplify the Expression: Remember that (i^2 = -1). So, we can replace (i^2) with (-1):
[ = ac + adi + bci - bd ]
Now, let’s put the real and imaginary parts together:
[ (ac - bd) + (ad + bc)i ]
By paying attention to the real (regular numbers) and imaginary (numbers with (i)) parts, you’ll correctly multiply complex numbers using the distributive property!