Question 1

What is a complex number?

Accepted Answer

A complex number is a number that can be expressed in the form `a + bi`, where `a` and `b` are real numbers, and `i` is the imaginary unit, which satisfies the equation `i² = -1`. In this expression, 'a' is the real part and 'b' is the imaginary part. Complex numbers are used in many areas of science and engineering, including electronics and signal processing.

Question 2

What is the imaginary unit 'i'?

Accepted Answer

The imaginary unit 'i' is the solution to the equation x² = -1. It is defined as the square root of negative one (√-1). Mathematicians created 'i' to solve problems that have no real number solution.

Question 3

How do you add or subtract complex numbers?

Accepted Answer

It's simple: you add or subtract the real parts and the imaginary parts separately. For example, `(3 + 2i) + (1 + 4i) = (3+1) + (2+4)i = 4 + 6i`.

Question 4

How do you multiply and divide complex numbers?

Accepted Answer

Multiplying is like using FOIL: `(a+bi)(c+di) = ac + adi + bci + bdi² = (ac-bd) + (ad+bc)i`. To divide, you multiply the top and bottom by the conjugate of the denominator. For `(a+bi)/(c+di)`, the conjugate is `(c-di)`.

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