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.
1 + i
Give your answer using the form z = A(cos(B°) + i sin(C°)).

 

A=

B=

C=

Answer 1

1 + i can be thought of as the vector from (0,0) to (1,1)

 

Draw a right triangle with vertices (0,0), (1,0), and (1,1)

 

A = distance from (0,0) to (1,1) = √[(1-0)² + (1-0)²] = √2

 

B = C = angle of the triangle formed by the x-axis and the vector                    

           = tan^-1(1/1) = 45°

 

1 + i = √2(cos45° + i sin45°)

Answer 2

Plot this number on the complex plane as stated in the instructions.

You can see that the angle created is π/4.

The modulus of the complex number is √2

 

1 + i = √2 (cos π/4 + i sin π/4)