Question

3-2i/1+3i /-знак дроби

Answer 1

$\frac{3 - 2i}{1 + 3i} \\ \\ \frac{(3 -2i) \times (1 - 3i)}{(1 + 3i) \times (1 - 3i)} \\ \\ \frac{3 - 9i - 2i + 6i {}^{2} }{1 - 9i {}^{2} } \\ \\ \frac{3 - 9i - 2i + 6 \times ( - 1)}{1 - 9 \times ( - 1)} \\ \\ \frac{3 - 9i - 2i - 6}{1 + 9} \\ \\ \frac{ - 3i - 9i - 2i}{1 + 9} \\ \\ \frac{ - 3 - 11i}{10} \\ \\ - \frac{3 + 11i}{10} \\ \\ - ( \frac{3}{10} + \frac{11}{10} i) \\ \\ - 0.3$

Answer 2

To simplify the expression (3 - 2i)/(1 + 3i), we need to get rid of the complex number in the denominator. To do that, we'll multiply both the numerator and denominator by the conjugate of the denominator.

The conjugate of 1 + 3i is 1 - 3i. Multiplying the expression by (1 - 3i)/(1 - 3i):

[(3 - 2i)/(1 + 3i)] * [(1 - 3i)/(1 - 3i)]

Now, let's perform the multiplication:

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

To expand the numerator and denominator:

Numerator: (3 - 2i)(1 - 3i) = 3 - 9i - 2i + 6i^2 = 3 - 11i - 6 (since i^2 = -1)

Numerator becomes: -3 - 11i

Denominator: (1 + 3i)(1 - 3i) = 1 - 3i + 3i - 9i^2 = 1 - 9i^2 (since i^2 = -1)

Denominator becomes: 1 + 9 = 10

So, the simplified expression is (-3 - 11i) / 10.