Question

find the module and arrangements the complex number 1+2i/1-3i​

Answer 1

Answer:

First we solve

1 + 2i

1- 3i

Let z = 1 + 2 i 1 - 3

Rationalizing the same

1 + 2i 1- 3i Х 1 + 3i 1+ 3i

(1+2i) (1+3i) (1- 3i) (1+ 3i)

1(1+3i) + 2i (1+ 3i) (1-3i) (1 + 3i)

1+ 3i + 2i + 6 i?

(1-3i)(1 + 3i)

Using (a - b) (a + b) = a2 - 62

1 + 5i + 6 i?

= (1)2 – (3i)?

1+ 5 i + 612

(1)2 – (31)2

1 + 5i + 6i? 1- 9i? 11

Putting i? = -1

1 + 5i + 6 (-1)

1-9 (-1)