a complex to real valued IFFT

if i have fft data from signal, that have symmetry property and then i have to multiply complex number.

when i multiply that, the output is not a symmetry. and ifft is the complex number

the reference book said that use a complex-to-real-valued IFFT to reduce computational complexity

what is a complex-to-real-valued IFFT??

(ex Hm(w) is filter and exp(im * theta)