The complex number in polar form will be z = √2(cos 45°+isin 45°)
Any complex number z = a + ib can be written in polar form as:
[tex]z = r(\cos(\theta) + i\sin(\theta))[/tex]
Raising this to nth power (n being an integer), we get:
[tex]z ^n = r^n (\cos(n\theta) + i\sin(n\theta))[/tex]
We know that Complex value z is written in a rectangular form as z = x+iy where (x, y) is the rectangular coordinates.
On converting the rectangluar to polar form of the complex number;
x = rcosθ and y = rsinθ
We need to Convert 1 + i to polar form,
The magnitude of the ray from the origin;
[tex]x^{2} +y^{2} = r^{2}[/tex]
[tex]r^{2}[/tex]= 1 + 1
r = √2
r is the modulus of the complex number and θ is the argument, θ = tan⁻¹y/x
θ = tan⁻¹ (1/1)
θ = tan⁻¹ (1)
θ = 45°
Hence the complex number in polar form will be z = √2(cos 45°+isin 45°)
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