Answer
Sum: $3i $
Product: $1+21i$
Work Step by Step
The sum of complex numbers can be expressed as:
$(a+bi)+(c+di)=(a+c)+\ i (b+d)$
Now, the required sum is:
$(3-2i)+(-3+5i)=[3+(-3)]+\ i (-2+5)=3i $
The product of complex numbers can be expressed as:
$(a+bi)\cdot(c+di)=ac+adi+bci-bd=(ac-bd)+\ i (bc+ad)$
Now, the required product is:
$(3-2i)(-3+5i)=3(-3)+3(5)i+(-2)i(-3)-(-2)5=-9+15i+6i+10=1+21i$
