Real and Imaginary Parts of z+(1/z) - Have I Got This Right?

In summary, the "real and imaginary parts" in an equation refer to the two components of a complex number, with the real part being the coefficient of the real number and the imaginary part being the coefficient of the imaginary number (represented by "i"). To determine these parts, the equation can be separated using the distributive property and solved individually. The real and imaginary parts can be fractions or decimals, and their values affect the overall value of the equation by determining the position of the complex number on the complex plane. If the real or imaginary part is equal to zero, the complex number is purely real or imaginary, respectively.
  • #1
kingyof2thejring
82
0
Hi there have i got this right if someone could check please? [tex]z=x+\imath{}y[/tex] Find the real and imaginary parts [tex]z+(1/z)[/tex] sub [tex]x+\imath{}y + \frac{1}{x+\imath{}y}[/tex] if we multiply by [tex]x+\imath{}y[/tex] and i get as the real part as [tex]x^2-y^2+1[/tex]. Have i got this right? Thanks in advance
 
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  • #2
No. First step.. I'd deal with the fractional part. Multiply the numerator and denominator by the complex conjugate of the denominator, and simplify. That's how you divide by a complex number anyway..
 
  • #3
cheers mate
 

1. What is the meaning of the "real and imaginary parts" in this equation?

The real and imaginary parts refer to the two components of a complex number. The real part is the coefficient of the real number, while the imaginary part is the coefficient of the imaginary number, represented by "i".

2. How do I determine the real and imaginary parts of this equation?

To determine the real and imaginary parts of this equation, you can use the distributive property to separate the equation into two parts. The first part will have only the real numbers, and the second part will have only the imaginary numbers. Then, you can solve for both parts separately.

3. Is it possible for the real and imaginary parts to be fractions or decimals?

Yes, it is possible for the real and imaginary parts to be fractions or decimals. In fact, most complex numbers have both a real and imaginary part that are not whole numbers.

4. What does it mean if the real or imaginary part is equal to zero?

If the real part is equal to zero, the complex number is purely imaginary and lies on the imaginary axis. If the imaginary part is equal to zero, the complex number is purely real and lies on the real axis.

5. How do the real and imaginary parts affect the overall value of the equation?

The real and imaginary parts of a complex number affect the overall value of the equation by determining the magnitude and direction of the number on the complex plane. The real part determines the horizontal position, while the imaginary part determines the vertical position.

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