Complex numbers

Eigenslate follows the standard notation for imaginary and complex number where "i" equals StartRoot, negative 1 , EndRoot. You can write complex numbers as a sum of real and imaginary components like 2 plus 3 "i".

By default, operations that can output a complex or imaginary number will give a complex or imaginary number. For example, the square root of a negative number will by default give the expected imaginary number instead of returning undefined.

StartRoot, negative 9 , EndRootequals 3 "i"

You can use "z" Superscript, "H" , Baseline to get complex conjugate of "z". This is the same notation used to take the hermitian transpose of a matrix.

left parenthesis, 2 plus 3 "i" , right parenthesis Superscript, "H" , Baselineequals 2 minus 3 "i"

You can take the absolute value of a complex number which returns the distance from 0 on the complex plane.

StartAbsoluteValue, 1 plus 1 "i" , EndAbsoluteValueequals 1.4 1 4 2 1

Type \Re (with a capital R) to take the real component of complex number, and type \Im (with a capital I) to get the imaginary component.

Recording of the calculator performing the steps described above