What is 4/(1+i)-2/(1-i) ?

The solution to 4/(1+i)-2/(1-i) is 1-3i

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simplify 4/(1+i)-2/(1-i)

simplify

\frac{4}{1 + i} - \frac{2}{1 - i}

1 - 3 i

Solution steps

\frac{4}{1 + i} - \frac{2}{1 - i}

\frac{4}{1 + i} = \frac{4 - 4 i}{2}

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

= \frac{4 - 4 i}{2} - \frac{2 + 2 i}{2}

\frac{4 - 4 i}{2} = 2 (1 - i)

\frac{2 + 2 i}{2} = 1 + i

= 2 (1 - i) - (1 + i)

Remove parentheses:

- (a + bi) = - a - bi

= 2 (1 - i) + - 1 - i

Expand

2 (1 - i) : 2 - 2 i

= 2 - 2 i - 1 - i

Group like terms

= - 2 i - i + 2 - 1

Add similar elements:

- 2 i - i = - 3 i

= - 3 i + 2 - 1

Subtract the numbers:

2 - 1 = 1

= - 3 i + 1

Rewrite in standard complex form:

1 - 3 i

= 1 - 3 i

x^{2} - 5 x + 4 \leq 0

3 x^{2} + 3 x - 60

4 \cdot (\frac{1}{2})^{- 1}

- 2 ∣ - x - 5 ∣ = - 10

∣ 4 - x ∣ < 5