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ololo11 [35]
3 years ago
10

Pt. 1 The result of adding a complex number to its conjugate is a.- a whole number b.-an integer, c.- a real number, d.- a pure

imaginary number Pt. 2 And the result of subtracting a complex number from its conjugate is a.- a whole number, b.-an integer, c.- a pure imaginary number, d.- a real number
Mathematics
1 answer:
Assoli18 [71]3 years ago
4 0

Answer:

Step-by-step explanation:

A complex number is a number that has both real and imaginary part. An example of a complex number is z = x+iy where x is the real part and y is the imaginary part.

If z = x+iy, the conjugate of z₁ will be x-iy

adding the complex number to its conjugate will give;

P = z+z₁

P = x+iy +(x-iy)

open the parenthesis

P = x+iy+x-iy

collect like terms

P = x+x+iy-iy

P = 2x

We can see that the resulting value does not contain the imaginary number i, hence the result is a real number.

<em>Hence the result of adding a complex number to its conjugate is a REAL NUMBER</em>

<em></em>

Taking the difference;

P =  = z-z₁

P = x+iy -(x-iy)

open the parenthesis

P = x+iy-x+iy

collect like terms

P = x-x+iy+iy

P = 0+2iy

P = 2iy

We can see that the resulting value contains the imaginary number i, hence the of taking their difference is a complex number.

<em>Hence the result of subtracting a complex number from its conjugate is an IMAGINARY NUMBER</em>

<em></em>

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