Multiplying and dividing real and complex numbers

In summary, multiplying two real numbers involves multiplying them together, while dividing complex numbers involves dividing the real and imaginary parts separately. Negative numbers can also be multiplied and divided, with the main difference being the result may be negative or positive depending on the number of negative numbers involved. The commutative property states that the order of numbers being multiplied or divided does not affect the result. To multiply and divide complex numbers in polar form, you simply perform the appropriate operations on the magnitudes and angles, and convert back to rectangular form if necessary for the final answer.
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Member warned to do some basic research before asking questions like this one
Is it possible to divide and multiply complex numbers and real numbers and if so, how does one do that? If not, why so? Cheers for your help!
 
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Multiplication: [itex](a+ib)(c+id)=ac-bd+i(ad+bc)[/itex]
Division: [itex]\frac{a+ib}{c+id}=\frac{(a+ib)(c-id)}{(c+id)(c-id)}=\frac{ac+bd+i(bc-ad)}{c^2+d^2}[/itex]
 
  • #4
If you know what "complex numbers" are then you should have seen how to do arithmetic with them.
 

1. How do I multiply two real numbers?

To multiply two real numbers, you simply need to multiply the two numbers together. For example, if you have 3 and 5, you would multiply 3 x 5 to get a product of 15.

2. What is the difference between multiplying and dividing complex numbers?

Multiplication of complex numbers involves multiplying the real and imaginary parts separately, while division involves dividing the complex numbers as a whole. Additionally, when dividing, you must also multiply the divisor by its complex conjugate to eliminate the imaginary component in the denominator.

3. Can you multiply and divide negative numbers?

Yes, you can multiply and divide negative numbers just like you would with positive numbers. The main difference is that if you multiply or divide an odd number of negative numbers, the result will be negative, while an even number of negative numbers will result in a positive number.

4. What is the commutative property in multiplication and division?

The commutative property states that the order of the numbers being multiplied or divided does not affect the result. For example, 3 x 5 is the same as 5 x 3, and 10 ÷ 2 is the same as 2 ÷ 10.

5. How do I multiply and divide complex numbers in polar form?

To multiply complex numbers in polar form, you simply multiply the magnitudes and add the angles. To divide, you divide the magnitudes and subtract the angles. It is important to convert back to rectangular form if necessary for the final answer.

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