My rental contract states that I need to give notice 'in writing' to my landlord prior to ending my tenancy. I'm new to legal terms and the country, does this phrase imply the notice needs to be filled in by hand and signed manually, or would an electronic copy of the notice with electronic signatures suffice?
"In writing" does not at all imply "written by hand". A typed or printed document is equally "in writing" and indeed is often preferred. These days an email or other electronic document is also considered to be "in writing", unless a contract specifies that notice must be made by postal mail, or some such requirement. If a document must be in writing and "signed" there are various ways of executing an electronic signature which are legally fully equivalent to a manual written signature. What thye requirement of notice in writing really means is that the notice cannot be spoken in person or by telephone, nor in any other way that does not involve some form of writing.
Canadian law distinguishes between the generic "electronic signature" and the "secure electronic signature". Federal secure electronic signature regulations make it clear that a secure electronic signature is a digital signature created and verified in a specific manner. Canada's Evidence Act contains evidentiary presumptions about both the integrity and validity of electronic documents with attached secure electronic signatures, and of the authenticity of the secure electronic signatures themselves.