Julia Quick Note [03] Complex Numbers

Complex number (example of writing)

note03

The imaginary unit is represented by im.
　z = 4 + 3im

◆ Real part
　real(z)

◆ Imaginary part
　imag(z)

◆ Complex conjugate
　conj(z)

◆ Absolute value
　abs(z)
　abs2(z)… A function that gets the square of the absolute value

Commentary

In mathematics, the complex number $ z $ is generally expressed as follows, with the complex number unit being $ i $, $ x $ and $ y $ as real numbers.

z = x + iy

In Julia, the imaginary unit can be $ im $ as well to represent complex numbers. For example, if the real part is 3 and the imaginary part is 4, it will be as follows.

z = 4 + 3im

◆ You can get the real part (real part) with real (z). ◆ You can get the imaginary part (imaginary part) with imag (z). ◆ To get the complex conjugate, use conj (z). ◆ Absolute value of complex number|z|To get abs(z)Use the. There is also a function ** abs2 () ** to get the square of the absolute value. This is convenient if you want to take the square.

: point_up_2: Julia allows you to perform four arithmetic operations on complex numbers.

addition subtraction multiplication division ◆ Confirm by numerical calculation that ① below holds.

z = 1 +As 2im\\
zz^* = x^2 + y^2 = |z|^2　　... ①

Calculating $ zz ^ * $ gives:

zz^* = (1 + 2im) * conj(1 + 2im) = 5

Also, if you calculate $ x ^ 2 + y ^ 2 $, it will be as follows.

x^2 + y^2 = 1 + 2^2 = 5

Finally,|z|^2Is calculated as follows. Therefore, ① was confirmed.

Lottery

Julia Quick Look Note [01] How to use variables and constants Julia Quick Look Note [02] Arithmetic Expressions, Operators [Julia Quick Note [03] Complex Numbers] (https://qiita.com/ttabata/items/225c77a4d71fafc3e482) Julia Quick Look Note [04] Regular Expression [Julia quick note [05] if statement] (https://qiita.com/ttabata/items/4f0bcff1e32f60402dfb)

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Related information

: paperclip: Julia --Official page https://julialang.org/

: paperclip: Julia --Japanese official document https://julia-doc-ja.readthedocs.io/ja/latest/index.html

: paperclip: First time Julia and installation (Windows & Linux) https://qiita.com/ttlabo/items/b05bb43d06239f968035

:paperclip: Julia - Mathematics https://docs.julialang.org/en/v1/base/math/

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