Let z is equal to 0 point 3 times open paren cosine of open paren 31 degrees close paren plus i sine open paren 31 degrees close paren close paren and w is equal to 20 times open paren cosine of open paren 18 degrees close paren plus i sine open paren 18 degrees close paren close paren Which statement describes the geometric construction of the product z w on the complex plane?
Answer
A
Stretch z by a factor of 20 , then rotate 49 degrees counterclockwise.
B
Stretch z by a factor of 6 , then rotate 49 degrees counterclockwise.
C
Stretch z by a factor of 6 , then rotate 18 degrees counterclockwise.
D
Stretch z by a factor of 20 , then rotate 18 degrees counterclockwise.
Explanation
To multiply complex numbers in trigonometric form, multiply their magnitudes and add their angles. The product has magnitude 0.3 × 20 = 6 and angle 31° + 18° = 49°. Thus, z is stretched by a factor of 6 and then rotated 49° counterclockwise.
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