Complex Number Formula

About Complex Number Formula

A complex number is one that satisfies the equation i2 = 1 and can be represented in the form a + bi, where a and b are real numbers and i is the imaginary unit. The real part of the complex number is a, while the imaginary part is b in this formula

By employing the horizontal axis for the real part and the vertical axis for the imaginary part, complex numbers extend the concept of the one-dimensional number line to the two-dimensional complex plane.

Here are some Complex Number formulas

  1. Equality of Complex Numbers Formula
    1. a + bi = c + di ⇔ a = c and b = d
  2. Addition of Complex Numbers
    1. (a + bi) + (c + di) = (a - c) + (b - d)i
  3. Subtraction of Complex Numbers
    1. (a + bi) - (c + di) = (a - c) + (b - d)i
  4. Multiplication of Complex Numbers
    1. (a + bi) × (c + di) = (ac - bd) + (ad - bc)i
  5. Multiplication Conjugates
    1. (a + bi)(a + bi) = a2 + b2
  6. Division of Complex Numbers
    1. complex
  7. Powers of Complex Numbers

1. in= i, if n = 4a+1, i.e. one more than the multiple of 4.

Solved example based on Complex Number Formula

Example:

i1 = i; i5 = i;i9 = i; i 4a + 1;

2. in= -1, if n = 4a+2, i.e. two more than the multiple of 4.

Example:

i2 = -1; i6 = -1; i10 = -1;i4a + 2

3. in= -i, if n = 4a+3, i.e. three more than the multiple of 4.

Example:

4. in= 1, if n = 4a, i.e. the multiple of 4. To get all the Maths formulas check out the main page. 

Pdf of Complex Number Formula

Complex Number Formula

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Frequently Asked Questions on Complex Number Formula