How to write in polar form

Now that we’ve discussed the polar form of a complex number we can introduce the second alternate form of a complex number. First, we’ll need Euler’s formula, With Euler’s formula we can rewrite the polar form of a complex number into its exponential form as follows.

The equation of polar form of a complex number z = x+iy is: z=r(cosθ+isinθ) where. r=|z|=√(x 2 +y 2) x=r cosθ. y=r sinθ. θ=tan-1 (y/x) for x>0. θ=tan-1 (y/x)+π or. θ=tan-1 (y/x)+180° for x<0 . Converting Rectangular form into Polar form. Let us see some examples of conversion of the rectangular form of complex numbers into polar form.

Adding Complex numbers in Polar Form. Suppose we have two complex numbers, one in a rectangular form and one in polar form. Now, we need to add these two numbers and represent in the polar form again. Let 3+5i, and 7∠50° are the two complex numbers. First, we will convert 7∠50° into a rectangular form. 7∠50° = x+iy.

Let us see some examples of conversion of the rectangular form of complex numbers into polar form. Example: Find the polar form of complex number 7-5i. Solution:7-5i is the rectangular form of a complex number. To convert into polar form modulus and argument of the given complex number, i.e. r and θ.