1. What is A+Bi Form?

The A+Bi form is the standard way to represent complex numbers, where 'A' is the real part and 'B' is the coefficient of the imaginary part (i). This form simplifies complex number operations and visualization.

2. How Does the Calculator Work?

The calculator simplifies complex numbers to standard form:

Where:

• \( a \) — Real part (unitless)
• \( b \) — Imaginary coefficient (unitless)
• \( i \) — Imaginary unit (\( \sqrt{-1} \))

Explanation: The calculator formats the complex number properly, handling cases where either part is zero, coefficients of 1, and proper sign placement.

3. Importance of Standard Form

Details: The A+Bi form is essential for complex number arithmetic, graphing on the complex plane, and understanding the relationship between real and imaginary components.

4. Using the Calculator

Tips: Enter the real and imaginary parts of your complex number. The calculator will properly format it according to mathematical conventions.

5. Frequently Asked Questions (FAQ)

Q1: What if my imaginary coefficient is zero?
A: The result will show only the real part (a + 0i simplifies to just a).

Q2: What if my real part is zero?
A: The result will show only the imaginary part (0 + bi simplifies to bi, or -bi if negative).

Q3: How are coefficients of 1 handled?
A: The calculator omits the coefficient when it's 1 (e.g., 1i becomes just i).

Q4: What about complex numbers in polar form?
A: This calculator works with rectangular form. For polar form conversion, you'd need a different tool.

Q5: Can I enter fractions or expressions?
A: Currently the calculator only accepts numerical inputs for a and b.