Finding sum of phasors when real components cancel out

[CE Trainee]

Homework Statement

I'm working on a problem where I have to add two phasors together. The problem is, the real parts cancel out and I can't figure out how to express the phase because arctan(y / 0) isn't defined.

Homework Equations

x1 = 10<45 degrees

x2 = 10<135 degrees

x1 + x2 = ?

The Attempt at a Solution

x1 in rectangular form = 7.07 + j7.07

x2 in rectangular form = -7.07 + j7.07

x3 = x1 + x2 = 0 + j14.14

x3 magnitude = 14.14

x3 phase = arctan( 14.14 / 0 )?

 

[rock.freak667]

The Attempt at a Solution

x1 in rectangular form = 7.07 + j7.07

x2 in rectangular form = -7.07 + j7.07

x3 = x1 + x2 = 0 + j14.14

x3 magnitude = 14.14

x3 phase = arctan( 14.14 / 0 )?

if x₃=14.14j, then it is purely imaginary and thus the vector is parallel to the imaginary plane. So the angle it makes with the real plane is just 90°.