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

March 28, 2026Mathematics

ScanSolve AI Answer

March 28, 2026

Answer

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

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 $(a+b)(a-b) = a^2 - b^2$ :

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Convert the complex number (1)/(1+i) to a+ib form. To do this, multiply the numerator and the denominator by the conjugate of the denominator.

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.

ScanSolve AI AnswerAnswered on March 28, 2026

Step 1: Convert the complex number (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. (1)/(1+i) = (1)/(1+i) × (1-i)/(1-i) Step 2: Perform the multiplication. The numerator becomes 1 × (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