Linear Algebra and Its Applications · Problem 1.3.29

Matrices and Gaussian Elimination — Gilbert Strang

Mathematics · gaussian-elimination

Problem

(Very optional) Normally the multiplication of two complex numbers

(a+ib)(c+id) = (ac-bd) + i(bc+ad)

involves the four separate multiplications

ac

bd

bc

ad

. Ignoring

i

, can you compute

ac-bd

and

bc+ad

with only three multiplications? (You may do additions, such as forming

a+b

before multiplying, without any penalty.)