Convert Complex Numbers in Trigonometric Form to Standard Form

These are the formulas that we will use to transform a complex number into standard form from trigonometric from.

Here we have our number in trigonometric form, z = r * (cos θ + i * sin θ). We must convert it to the form z = a + b * i. We know a = r * cos θ and b = r * sin θ . Since θ e quals π , we can substitute π into both cosine and sin e.

Now we go back to the standard form of a complex number, z = a + bi. We know a = -5 and b = 0 so we substitute both numbers so z = -5 + 0i. Our final answer is z = -5.

Here we have our number in trigonometric form, z = r * (cos θ + i * sinθ). We must convert it to the form z = a + b * i. We know a = r * cos θ and b = r * sin θ.

In this case we don't have an exact value for θ. W e have to use θ = tan -1 (3). Now, we have to work backwards and draw to find the modulus of z or r or the distance from the origin to our point.

We know tangent = the opposite side length over the adjacent side length. Since θ = tan -1 (3), we tan both sides to get, tan θ = 3 or tan θ = 3 /1. So the opposite side length is 3 and the adjacent side length is 1. We can draw our lines on the coordinate to form a triangle.