Question

1+3i/1_2i write in polar from​

Answer 1

$\frac{1 + 3i}{1 - 2i}$

now rationalise it

then ,

you get

-1+ i

$\tan(theta) = \frac{ |y| }{ {x} }$

then

$\tan(theta) = 1$

then

theta = π/4= tan^-1(y/X)

we have z = -x +iy

therefore theta

$\pi - \tan {}^{ - 1} ( \frac{y}{x} )$

$\frac{3\pi}{4}$

modulus of complex no

$|z| = \sqrt{2}$

hence polar form =

$|z| ( \cos(theta) + i \sin(thet) )$

then ,

polar form :

=

$\sqrt{2} ( \cos( \frac{3\pi}{4} ) + i \sin( \frac{3\pi}{4} ) )$

I hope it help you ❤️

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