Define complex numbers. Give definitions of sum and product of two complex numbers?

Answer 1

Complex numbers is the sum of real numbers and imaginary numbers. Imaginary numbers are real numbers multiplied by the square root of -1.

The sum and product of two conjucate complex numbers always equals to a real number. (a + bi and a - bi)

Answer 2

A complex number has both a real and an imaginary component. a+bi is a complex number having the real component = a and the imaginary component bi where b is real, but i = sqrt (-1) and is imaginary.

(3+4i) + (2 + 6i) = 5 + 10i ( just add rel to real and imaginary to imaginary. Similarly (3+4i)-(2+6i) = (1 -2i).

If a = 0, the number is pure imaginary. If b = 0 the number is real If bith a and b are real, then the number is complex.

Answer 3

A complex number is the sum of a real number and an imaginary one. The imaginary part of it is the product of a real number and i, the square root of -1.

The sum of two complex numbers:

(a + bi) + (c + di) = (a + d) + (b + ci)

(a + bi)*(c + di) = ac + bci + adi + bi*di =
= ac + bci+ adi + bdi*i = ac + bci + adi - bd =
= (ac - bd) + (ad + bc)i