The product (2 + bi)(3 + 2i) is equal to 13i. What is the value of b?

Step-by-step explanation:

Lets FOIL it out:

6+4i+3bi+2bi²=13i

6-4i-13i+3bi+2bi²=0

6-9i+3bi+2bi²=0,but i²=-1

3bi-2b=9i-6

b(3i-2)=9i-6

Divide both sides by (3i-2)

b=(9i-6)/(3i-2)

Rationalize the expression by multiplying through by the conjugate of (3i-2) which is (3i+2)

b=(27i²+18i-18i-12)/(9i²+6i-6i-4),again i²=-1

b=27i²-12/9i²-4

b=-27-12/-9-4

b=-39/-13

b=3