Question

Express[1+2i] divied by[1-2i] in polar form

Answer 1

Answer:

Answer:

\sqrt{2}e^{i\frac{3\pi}{4}}

2

e

i

4

3π

Step-by-step explanation:

The given equation is:

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

We have to convert the given equation in the polar form, thus

={\frac{1+3i}{1-2i}{\times}\frac{1+2i}{1+2i}}

1−2i

1+3i

×

1+2i

1+2i

={\frac{1+5i-6}{1+4}}

1+4

1+5i−6

={\frac{-5+5i}{5}}

5

−5+5i

=-1+i−1+i

={\sqrt{2}{\times}{\frac{1}{\sqrt{2}}(-1+i)

=\sqrt{2}(\frac{-1}{\sqrt{2}}+\frac{1}{\sqrt{2}}i)

2

(

2

−1

+

2

1

i)

=\sqrt{2}(cos({\pi}-{\frac{\pi}{4})+isin({\pi}-{\frac{\pi}{4}))

=\sqrt{2}(cos{\frac{3\pi}{4}+isin{\frac{3\pi}{4})

=\sqrt{2}e^{i\frac{3\pi}{4}}

2

e

i

4

3π

which is the required polar form.