The imaginary unit along the vertical axis is represented in MuPAD by the symbol I in the input and an upright i in the typeset output.
You can input complex numbers in the usual mathematical notation \(x + y i\) . Note that in engineering and computer science, the unit vector in the vertical direction is denoted by j but not i. Both
the real part \( x \) and the imaginary part \( y \) may be integers, rational numbers, or
floating-point numbers:
(1 + 2*I)*(4 + I), (1/2 + I)*(0.1 + I/2)^3
2 + 9 i, 0.073 − 0.129 i
If you use symbolic expressions such as, e.g., sqrt(2), MuPAD may not return the
result of a calculation in Cartesian coordinates:
1/(sqrt(2) + I)
\[
\frac{\sqrt{2}}{3} - \frac{i}{3}
\]
The functions Re and Im return the real part \(x \) and the imaginary part \( y \) ,
respectively, of a complex number \(x + y i\) . The functions conjugate, abs, and arg
compute the complex conjugate \(x - y i\) , the absolute value \( |x + y i | = \sqrt{x^2 + y^2}\) ,
and the polar angle, respectively:
Re(1/(sqrt(2) + I)), Im(1/(sqrt(2) + I)),
conjugate(1/(sqrt(2) + I)),
abs(1/(sqrt(2) + I)), arg(1/(sqrt(2) + I)),
rectform(conjugate(1/(sqrt(2) + I)))
\[
\frac{\sqrt{2}}{3} , \quad -\frac{1}{3} , \quad \frac{1}{\sqrt{2} -i}
, \quad \frac{\sqrt{3}}{3} , \quad -\arctan \left( \frac{\sqrt{2}}{2}
\right) , \quad \frac{\sqrt{2}}{3} + \frac{i}{3}
\]