math hw help is appreciated

Question

How is the product of a complex number and a real number represented on the coordinate plane?

A)When 2 + 3i is multiplied by 3, the result is 6 + 9i. Graphically, this shows that the product is a clockwise rotation of 90° of the complex number.

B) When 2 + 3i is multiplied by 3, the result is 6 + 9i. Graphically, this shows that the product is a scalar of the complex number

C) When 2 + 3i is multiplied by 3, the result is 6 + 9i. Graphically, this shows that the product is a counterclockwise rotation of 90° and a scalar of the complex number.

D) When 2 + 3i is multiplied by 3, the result is 6 + 9i. Graphically, this shows that the product is a counterclockwise rotation of 90° of the complex number.

Answer 1

B) It's a scalar product

there is no rotation

plot i on the y axis and plot real numbers on the x axis

3i+2 is the same point basically as (3,2) on a axes with just real numbers

3(3i+2) = 9i+6 just like 3(3,2) = (9,6)

3i+2 is a vector

9i+6 has the same vector's direction, but with 3 times the magnitude

(Meanwhile there's a related math joke: Why couldn't Sir Hillary and Typhoid Mary have children? Because you can never cross a vector with a scalar---it's a pun on the meaning of a disease vector and a mountain scalar, okay, it's not funny, but it's not funny/humorous as in late night TV comedy, but "funny"/weird in a mathematics way. something you learn at least by Calculus III. "Hillary" means Edmund Hillary not Hillary Clinton although she famously falsely claims she was named after him. but then who knows, maybe her mother was just trying to inspire her and tell her she could climb any mountain. Plus "Sir Hillary for Hillary Clinton seems prophetic of the pronoun controversy of LGBTQ)