Convert the complex number (1)/(1+i) to a+ib form.

Question

Convert the complex number (1)/(1+i) to a+ib form.

Asked on March 28, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-03-28T23:35:13.251Z

Step 1: Convert the complex number $\frac{1}{1+i}$ to $a+ib$ form. To do this, multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of $1+i$ is $1-i$. $$ \frac{1}{1+i} = \frac{1}{1+i} \times \frac{1-i}{1-i} $$ Step 2: Perform the multiplication. The numerator becomes $1 \times (1-i) = 1-i$. The denominator becomes $(1+i)(1-i)$. Using the difference of squares formula $(a+b)(a-b) = a^2 - b^2$: $$ (1+i

Accepted Answer · 2026-03-28T23:35:13.251Z

Step 1: Convert the complex number $\frac{1}{1+i}$ to $a+ib$ form. To do this, multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of $1+i$ is $1-i$. $$ \frac{1}{1+i} = \frac{1}{1+i} \times \frac{1-i}{1-i} $$ Step 2: Perform the multiplication. The numerator becomes $1 \times (1-i) = 1-i$. The denominator becomes $(1+i)(1-i)$. Using the difference of squares formula $(a+b)(a-b) = a^2 - b^2$: $$ (1+i