Plot this complex number in the complex plane and write it in polar form.

Question

 Plot this complex number in the complex plane and write it in polar form. Express the argument in degrees.
3 - 4i
Give your answer using the form z = A(cos(B°) + i sin(C°)).

 

A=

B=

c=

Answer 1

3 - 4i can be thought of as the vector from (0,0) to (3, -4).

 

Draw a right triangle with vertices (0,0), (3,-4), and (3,0).

 

A = distance from (0,0) to (3, -4) = √[(3-0)² + (-4-0)²] = 5

 

θ = acute angle of the triangle formed by the x-axis and vector

 

   = tan^-1(4/3) = 53.13°

 

B = C = 360° - 53.13° = 306.87°

 

3 - 4i = 5(cos306.87° + i sin306.87°)