simplify 1/(1+i) — step-by-step solution

Let's reduce:

\frac{1}{1 + i}

ⓘ To make the denominator real, multiply the numerator and denominator by its conjugate, since (a+bi)(a-bi) = a²+b²:

\frac{1}{1 + i}

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

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

ⓘ The numerator and the denominator are computed before the division:

1 + 1

2

\frac{1 - i}{2}

ⓘ A complex number is written in algebraic form a + b*i, a being its real part and b its imaginary part:

\frac{1 - i}{2}

\frac{1}{2} - \frac{1}{2} \times i

▶Simplified form:

\frac{1}{2} - \frac{1}{2} \times i

The numeric value of:

\frac{1}{2} - \frac{1}{2} \times i

is:

▷

0.5 - 0.5 i