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

When 6 + 4i is multiplied by 3, the result is 18 + 12i. Graphically, this shows that the product is a scalar and a 90° counterclockwise rotation of the complex number.

When 6 + 4i is multiplied by 3, the result is 18 + 12i. Graphically, this shows that the product is a scalar of the complex number.

When 6 + 4i is multiplied by 3, the result is 18 + 12i. Graphically, this shows that the product is a scalar and a 90° clockwise rotation of the complex number.

When 6 + 4i is multiplied by 3, the result is 18 + 12i. Graphically, this shows that the product is a 90° counterclockwise rotation of the complex number.

Consider the series 1/4 + 1/6 + 1/9 + 2/27 + 4/81 +....

Does the series converge or diverge?

Select answers from the drop-down menus to correctly complete the statements.

The series __________ (converges or diverges). You can conclude this because the series is _______________ (arithmetic. geometric and the absolute value of the common ratio is greater than 1. geometric and the absolute value of the common ratio is less than 1. or neither arithmetic nor geometric.)

A 0

B 1/3

C 3

D The limit does not exist.

Guest Jun 9, 2021

#1**+1 **

First one

When 6 + 4i is multiplied by 3, the result is 18 + 12i. Graphically, this shows that the product is a scalar of the complex number.

Second one

Converges (gets smaller and smaller)

Geometric and the absolute value of the common ratio is less than 1 (=2/3)

Last one

The limit is just the ratio of the coefficients on the n^4 terms in the numerator and denominator = 2/6 = 1/3

CPhill Jun 9, 2021