"Echt komplex" in English?

Question

In German, we sometimes use the term "echt komplex" for complex numbers which aren't real, i.e. for complex numbers with a non-vanishing imaginary part. Is there an English equivalent for this? (I obviously don't mean purely imaginary.)

Answer 1

Actually, I have sometimes seen a different definition for "echt komplex". Let $z=a+bi$ a complex number. Then we have three cases.

Case 1: If $a=0$, then $z$ is called "rein imaginär" (purely imaginary).

Case 2: If $b=0$, then $z$ is called "rein reell" (purely real).

Case 3: If both $a,b$ are nonzero, then $z$ is called "echt komplex".

Edit: There are also references, which define for a complex number $z$, that $z$ is "echt komplex" if and only if it is non-real. For this interpretation the answer to the question is then just: $z$ is non-real". I have never seen "genuinely complex", or "typically complex".

Answer 2

"Echt" has passed from German to English, meaning "typical" or "authentic" in both languages. So complex numbers with both parts nonzero are considered the "typical" case in the context where "echt komplex" is used in German.