Multiplying and dividing real and complex numbers

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Discussion Overview

The discussion centers on the operations of multiplication and division involving complex numbers and real numbers. It explores the methods for performing these operations and the underlying principles of complex arithmetic.

Discussion Character

  • Technical explanation

Main Points Raised

  • One participant confirms that it is possible to multiply and divide complex and real numbers.
  • Another participant provides the formulas for multiplying and dividing complex numbers, detailing the steps involved in the division process.
  • A different participant suggests that familiarity with complex numbers implies knowledge of how to perform arithmetic operations with them.

Areas of Agreement / Disagreement

Participants generally agree that multiplication and division of complex and real numbers are possible, but the depth of understanding and methods may vary among them.

Contextual Notes

Some assumptions about prior knowledge of complex numbers and arithmetic operations are present, which may limit the discussion for those unfamiliar with the topic.

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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]
 
If you know what "complex numbers" are then you should have seen how to do arithmetic with them.
 

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