Scalar Multiplication

Scalar Multiplication

If $z=a+ib$ is any complex number, then for every real number $k$, scalar multiplication is defined by

— multiplying a complex number by a real scalar $k$ multiplies both its real and imaginary parts by that same $k$.

Worked examples.

1. If $z=7+3i$, then $5z=5(7+3i)=35+15i$.
2. If $z_1=3-4i$ and $z_2=10-9i$, then $2z_1+5z_2=2(3-4i)+5(10-9i)=(6-8i)+(50-45i)=56-53i$. …