Question

write-1+2i in polar form​

Answer 1

Answer:

I know r=√5, and when using x=rcosθ, I get angle of 63.43 or 296.57. However, when I take the sin inverse of-2/√5 I get -63.43. I am really confused.

Source https://www.physicsforums.com/threads/1-2i-in-polar-form.670136/

Answer 2

Answer:

-1 + 2i can be written as $\sqrt{5}$( cos 243.43° + i sin 243.43°)

Step-by-step explanation:

Given the complex number -1 + 2i

As it is a complex number, let it be equal to x + iy

On equating the real and imaginary parts, we get,

x = -1 and y = 2

To convert the number in polar form, we find r and $\theta$

where r = $\sqrt{x^{2} + y^{2}}$

and $\theta$ = tan⁻¹ ( $\frac{y}{x}$ )

Here, r = $\sqrt{(-1)^{2} + 2^{2}}$ = $\sqrt{1+4}$ = $\sqrt{5}$

and $\theta$  = tan⁻¹ ( $\frac{2}{-1}$ ) = tan⁻¹ ( $\frac{2}{1}$ ) + π  (as x < 0)

=> $\theta$  = 63.43 + 180

=> $\theta$  = 63.43 + 180

=> $\theta$  = 243.43

We know that x + iy can be written as r(cos $\theta$  + i sin $\theta$ )

=> -1 + 2i can be written as $\sqrt{5}$( cos 243.43° + i sin 243.43°)