Write the complex number in trigonometric form, once using degrees and once using radians. Begin by sketching the graph to help find the argument 𝜃.−1 + i

Sure, let's start by understanding the complex number -1 + i.

Step 1: Plot the complex number on the complex plane The real part of the complex number is -1 and the imaginary part is 1. So, we plot a point at (-1, 1) on the complex plane.

Step 2: Find the magnitude (r) of the complex number The magnitude of a complex number a + bi is given by √(a² + b²). So, the magnitude of -1 + i is √((-1)² + 1²) = √2.

Step 3: Find the argument (θ) of the complex number The argument of a complex number a + bi in the first and fourth quadrants is given by arctan(b/a). But since our complex number is in the second quadrant, we need to add π (or 180°) to this. So, θ = arctan(1/-1) + π = π/4 + π = 5π/4 in radians or 225° in degrees.

Step 4: Write the complex number in trigonometric form The trigonometric form of a complex number a + bi is r(cos θ + i sin θ). So, the trigonometric form of -1 + i is √2(cos(5π/4) + i sin(5π/4)) in radians or √2(cos(225°) + i sin(225°)) in degrees.