4
QuizMultiple Choice

Add and Subtract Complex Numbers — Quiz

Question 4 • Math 4

Consider w is equal to 4 times open paren cosine of open paren pi over 2 close paren plus i sine open paren pi over 2 close paren close paren and z is equal to 3 times open paren cosine of open paren 3 pi over 2 close paren plus i sine open paren 3 pi over 2 close paren close paren What is w plus z expressed in polar form?

Answer
A
cosine of open paren pi over 2 close paren plus i sine open paren pi over 2 close paren
B
cosine of pi plus i sine pi
C
cosine of open paren 3 pi over 2 close paren plus i sine open paren 3 pi over 2 close paren
D
cosine of 0 plus sine of 0

Explanation

Using the standard angles, cos(π/2) = 0 and sin(π/2) = 1, so w = 4i. Also, cos(3π/2) = 0 and sin(3π/2) = −1, so z = −3i. Therefore, w + z = i, which has modulus 1 and angle π/2. Its polar form is cos(π/2) + i sin(π/2), the choice that gives the correct result.

AI-written and checked against the verified answer.

Previous
Next