Question

sejam Z¹ = 1 + 2i e Z² = 1 - i. Calcule Z¹/Z²

Answer 1

Sejam

Z¹ = 1 + 2i

Z² = 1 - i.

Calcule Z¹/Z²

Z¹

----

Z²

(1 + 2i)

-----------

(1 - i)

(1 + 2i)(1 + i)

-------------------

(1 - i)(1 + i)

1 + 1i + 2i + 2i²

-----------------------

1 + 1i - 1i - i²

1 + 3i + 2i²

-------------------

1 + 0 - i²

1 + 3i + 2i²

--------------------- lembrando que (i² = - 1)

1 - i²

1 + 3i  + 2(- 1)

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1 - (-1)

1 + 3i - 2

--------------

1 + 1

1 - 2 + 3i

----------------

2

- 1 + 3i

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