Multiply Complex Numbers

The complex number consists of imaginary part and real part is defined as the complex number.

The complex number is written the form x + yi where x and y are real numbers and i is defined as the imaginary unit.

The normal numbers in the complex numbers is extended by using extra numbers.

The complex numbers are used in quantum physics, engineering and applied mathematics.

Multiply Complex Number:

Multiplication: (a + bi)(c + di) = (ac - bd) + (bc + ad)i

Examples on Multiply Complex Numbers:

Example 1:

Solve (2 + 2i)(5 + 3i)

Solution:

The multiplication of the complex numbers in the arithmetic form is given as,

(2 + 2i)(5 + 3i) = 10 + 6i + 10i + 6i^2

= 10 + 16i - 6   { Since i^2  = -1 }

= 4 + 16i.

The complex number multiplication answer is 4 + 16i.

Example 2:

Solve

(3 + 7i)(4 + 3i)

Multiplication of the complex number in algebraic form is given as,

(3 + 7i)(4 + 3i) = 12 + 9i + 28i + 21i^2

= 12 + 37i - 21

= -9 + 37i.

These are examples of multiplication of complex numbers.

Hence the complex number multiplications answer is -9+37i.

Example 3:

Solve

(4 + 7i)(3 + 3i)

Multiplication of the complex number in algebraic form is given as,

(4 + 7i)(3 + 3i) = 12 + 21i + 12i + 21i^2

= 12 + 33i - 21

= -9 + 33i.

These are examples of multiplication of complex numbers.

Hence the complex number multiplications answer is -9+33i.

Example 4:

Solve

(4 + 3i)(3 + 7i)

Multiplication of the complex number in algebraic form is given as,

(4 + 3i)(3 + 7i) = 12 + 9i + 28i + 21i^2

= 12 + 37i - 21

= -9 + 37i.

These are examples of multiplication of complex numbers.

Hence the complex number multiplications answer is -9+37i.

Example 5:

Solve

(2 + 5i)(4 + 6i)

Multiplication of the complex number in algebraic form is given as,

(2 + 5i)(4 + 6i) = 8 + 20i + 12i + 30i^2

= 8 + 32i - 30

= -28 + 32i.

These are examples of multiplication of complex numbers.

Hence the complex number multiplications answer is -28+32i.