Imaginary unit
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Syntax
1j
z = a + bj
z = x +1j*y
Description
1j returns the basic imaginary unit. j isequivalent to sqrt(-1).
You can use j to enter complex numbers.You also can use the character i as the imaginaryunit. To create a complex number without using i and j,use the complex function.
z = a + bj returnsa complex numerical constant, z.
example
z = x +1j*y returns a complex array, z.
example
Examples
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Complex Scalar
Open Live Script
Create a complex scalar and use the character, j, without a multiplication sign as a suffix in forming a complex numerical constant.
z = 1+2j
z = 1.0000 + 2.0000i
Complex Vector
Open Live Script
Create a complex vector from two 4-by-1 vectors of real numbers. z is a 4-by-1 complex vector.
x = [1:4]';y = [8:-2:2]';z = x+1j*y
z = 4×1 complex 1.0000 + 8.0000i 2.0000 + 6.0000i 3.0000 + 4.0000i 4.0000 + 2.0000iComplex Exponential
Open Live Script
Create a complex scalar representing a complex vector with radius, r, and angle from the origin, theta.
r = 4;theta = pi/4;z = r*exp(1j*theta)
z = 2.8284 + 2.8284i
Input Arguments
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a — Real component of complex scalar
scalar
Real component of a complex scalar, specified as a scalar.
Data Types: single | double
b — Imaginary component of complex scalar
scalar
Imaginary component of a complex scalar, specified as a scalar.
If b is double, you canuse the character, j, without a multiplicationsign as a suffix in forming the complex numerical constant.
Example: 7j
If b is single, you mustuse a multiplication sign when forming the complex numerical constant.
Example: single(7)*j
Data Types: single | double
x — Real component of complex array
scalar | vector | matrix | multidimensional array
Real component of a complex array, specified as a scalar, vector, matrix, or multidimensional array.
The size of x must match the size of y,unless one is a scalar. If either x or y isa scalar, MATLAB® expands the scalar to match the size of theother input.
single can combine with double.
Data Types: single | double
y — Imaginary component of complex array
scalar | vector | matrix | multidimensional array
Imaginary component of a complex array, specified as a scalar, vector, matrix, or multidimensional array.
The size of x must match the size of y,unless one is a scalar. If either x or y isa scalar, MATLAB expands the scalar to match the size of theother input.
single can combine with double.
Data Types: single | double
Output Arguments
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z — Complex array
scalar | vector | matrix | multidimensional array
Complex array, returned as a scalar, vector, matrix, or multidimensionalarray.
The size of z is the same as the input arguments.
z is single if at leastone input argument is single. Otherwise, z is double.
Tips
For speed and improved robustness in complex arithmetic,use
1iand1jinstead ofiandj.Since
jis a function, it canbe overridden and used as a variable. However, it is best to avoidusingiandjfor variable namesif you intend to use them in complex arithmetic.Use the
complexfunction to createa complex output in the following cases:When the names
iandjmightbe used for other variables (and do not equalsqrt(-1))When the inputs are not
doubleorsingleWhen the imaginary component is all zeros
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.
Thread-Based Environment
Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.
This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.
Version History
Introduced before R2006a
See Also
conj | complex | imag | i | real
Topics
- Create Complex Numbers
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