Write the complex number in polar form with argument θ between 0 and 2π. −7 + 7i

It can be helpful to draw a diagram, or at least think about what such a diagram would look like. The point is in the 2nd quadrant, so the angle will be more than π/2 and less than π. You may recognize that the reference angle is 45°, and that the distance to the origin is 7√2. If not, those things can be calculated.

Number magnitude = √((real part)² +(imaginary part)²)
  = √((-7)² +(7)²) = √98
Number magnitude = 7√2

Number angle = arctan((imaginary part)/(real part)) . . . . . considering quadrant
    = arctan(7/-7) = arctan(-1) . . . . . in the second quadrant
Number angle = 3π/4

In polar form, -7 +7i = (7√2)∠(3π/4 radians)

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