Question

1) Efetue a divisão: z=2+3i w=10 - 5i 5 + 4i 5 - 25i 1 + 30i / 25 10 + 30i / 50

Answer 1

Explicação passo-a-passo:

2−i

−10+15i

.

(2+i)

(2+i)

=

4+2i−2i−i

2

−20−10i+30i+15i

2

=

4−(−1)

20i−20+15(−1)

=

4+1

20i−20−15

=

5

−35+20i

=

5

−35

+

5

20i

=

−7+4i

b)

\begin{lgathered}\frac{1+3i}{1+i}. \frac{(1-i)}{(1-i)} = \frac{1-i+3i-3i^2}{1-i+i-i^2} =\\\\ \frac{1+2i-3(-1)}{1-(-1)}= \frac{1+2i+3}{1+1} = \frac{4+2i}{2} = \frac{4}{2} + \frac{2i}{2} =\boxed{2+i}\end{lgathered}

1+i

1+3i

.

(1−i)

(1−i)

=

1−i+i−i

2

1−i+3i−3i

2

=

1−(−1)

1+2i−3(−1)

=

1+1

1+2i+3

=

2

4+2i

=

2

4

+

2

2i

=

2+i