complex numbers notation Watch
Re(z) = a
Im(z) = b???
im(z) = bi.
Do you know argand diagrams?
Think about the real and imaginary part as the displacement in the real axis and imaginary axis. Displacement is a real number, so the imaginary part is a real number.
So we have real numbers which are complex numbers with a 0 imaginary part. I'd reccomend avoiding the term "imaginary numbers" and use the term "pure imaginary" when denoting a complex number with a 0 real part.
so terms to learn
Complex number ( a+bi) - made up of the real part (a) and the imaginary part (b) where a and b are real numbers.
real number - a complex number with 0 imaginary part.
pure imaginary number -
a complex number with 0 real part.