# Perl ABC

## Representing complex numbers/Statistical analysis by PDL

Complex numbers are represented using the i function, which represents the imaginary unit that becomes available when you read PDL::Complex .

For example, to represent the complex number 3 + 2i :

```use PDL;
use PDL::Complex;

my \$num = 3 + 2 * i;
```

When this complex number is output, it will be displayed as follows.

```3 + 2i
```

### Use the imaginary unit i

PDL can handle imaginary numbers. To handle imaginary numbers, load PDL::PDL::Complex .

```use PDL::Complex;
```

Then the i function that represents the imaginary unit is imported.

```i
```

When the imaginary unit is output, it is output as follows.

```0 + 1i
```

The imaginary unit i was a number that squared to -1. Let's square it.

```my \$ret = i * i;
```

When this is output, it will be displayed as follows.

```-1 + 0i
```

### Four arithmetic operations on complex numbers

Perform four arithmetic operations on complex numbers using + , -, * , / as in normal operations. I can.

```use PDL;
use PDL::Complex;

my \$num1 = 1 + 2 * i;
my \$num2 = 3 + 4 * i;
```

#### Japanese

```# 4 + 6i
my \$sum = \$num1 + \$num2;
```

#### Difference

```# 2 + 2i
my \$sub = \$num2- \$num1;
```

#### Product

```# -5 + 10i
my \$multi = \$num1 * \$num2;
```

#### Commerce

```# 0.44 + 0.08i
my \$div = \$num1/\$num2;
```

### Calculate the nth root

Use the Croots function to calculate the nth root.

```use PDL;
use PDL::Complex;

# 5 cube root
my \$nums = Croots (5, 3);
```

The output of the calculation result is as follows.

```[1.85398 + 0.496773i -1.35721 + 1.35721i -0.496773 -1.85398i]
```

### Convert real numbers to complex numbers

Use the r2C function to convert a real number to a complex number.

```use PDL;
use PDL::Complex;

my \$num = r2C 5;
```

The output result is as follows.

```5 + 0i
```