Chapter 14: Q5P (page 667)

Find the real and imaginary parts $u (x, y)$ and $v (x, y)$ of the following functions.
$Re z$

Short Answer

Expert verified

The real part $u (x, y)$ of the function is x , and the imaginary part $v (x, y)$ of the function is 0.

Step by step solution

Definition of complex numbers

Complex numbers are expressed in the form of $z = x + i y$ , where x,y are real numbers, and i is an imaginary number.

Similarly, the function of z is represented as follows:

$f (z) = f (x + i y) = u (x, y) + i v (x, y)$

, where $u (x, y)$ is the real part and $v (x, y)$ is the imaginary part.

Substitute the value in the given function.

The given function is $Re z$ .

Substitute $z = x + i y$ in $Re z$ as follows:

$Re z = Re (x + i y) = x = x + 0 i$

The above equation is in the form of $f (z) = f (x + i y) = u (x, y) + i v (x, y)$ , such that $u (x, y) = x$ and $v (x, y) = 0$ .

Hence, the real part of the given function is $u (x, y) = x$ , and the imaginary part is $v (x, y) = 0$ .

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Find the real and imaginary parts $u (x, y)$ and $v (x, y)$ of the following functions.
$Re z$

Short Answer

Step by step solution

Definition of complex numbers

Substitute the value in the given function.

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Find the real and imaginary parts u(x,y)and v(x,y)of the following functions.Rez

Short Answer

Step by step solution

Definition of complex numbers

Substitute the value in the given function.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Classical Mechanics

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Study anywhere. Anytime. Across all devices.

Find the real and imaginary parts $u (x, y)$ and $v (x, y)$ of the following functions.
$Re z$