The polar form of complex number  5−3i4+i5−3𝑖4+𝑖 is (where i =  √–1–1)

To find the polar form of a complex number, we first need to find the magnitude (r) and the angle (θ) of the complex number.

The complex number is given as z = 5 - 3i / 4 + i.

Step 1: Calculate the magnitude (r) The magnitude of a complex number z = x + yi is given by r = √(x² + y²). Here, x = 5 and y = -3. So, r = √((5)² + (-3)²) = √(25 + 9) = √34.

Step 2: Calculate the angle (θ) The angle of a complex number z = x + yi is given by θ = atan(y/x). Here, x = 5 and y = -3. So, θ = atan(-3/5) = -0.5404 radians.

Step 3: Write the polar form The polar form of a complex number is given by z = r(cos θ + i sin θ). So, the polar form of the given complex number is z = √34(cos(-0.5404) + i sin(-0.5404)).

Please note that the angle is usually expressed in degrees. The conversion from radians to degrees is done by multiplying the angle in radians by 180/π. So, -0.5404 radians is approximately -31 degrees. Therefore, the polar form can also be written as z = √34(cos(-31°) + i sin(-31°)).