to multiply two complex numbers such as (2 + 3i)(3 + 5i), we can use the ________ method?

distribution

There are 2 ways 1-rectangular method, just multiply the terms as regular #, with i^2=-1.

6+10i+9i-15=-9+19i

2-polar method, convert each parenthesis to polar form.

2+3i=sqrt(2^2+3^2)@angle(arctan(3/2)=3.6 @56.3deg, 3+5i=5.83 @59 deg

then multiply the 2 magnitudes and add the two angles = 20.98 @115deg.

The 3 answs are equal..notice that -64deg=115deg. Try to convert them yourself.

Rectangular tells you that the product of these 2 vectors (expression in parenthesis) is another vector from 0,0 to -9,19. The polar tells you that its a vector w/ magnitude (length)=21 at angle of -64 or +115.