Multiply 9 + -6i and 2 + -4i

Publish date: 2024-06-04

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Evaluate this complex number multiplication

(9 - 6i)(2 - 4i)

Define the FOIL Formula:

(a * c) + (b * c) + (a * d) + (b * d)

Set the FOIL values:

a = 9, b = -6, c = 2, and d = -4

Plug in values:

(9 - 6i)(2 - 4i) = (9 * 2) + (-6i * 2) + (9 * -4i) + (-6i * -4i)

(9 - 6i)(2 - 4i) = 18 - 12i - 36i + 24i2

Group the like terms:

(9 - 6i)(2 - 4i) = 18 + (-12 - 36)i + 24i2

(9 - 6i)(2 - 4i) = 18 - 48i + 24i2

Simplify our last term:

i2 = √-1 * √-1 = -1, so our last term becomes:

(9 - 6i)(2 - 4i) = 18 - 48i + 24* (-1)

(9 - 6i)(2 - 4i) = 18 - 48i - 24

Group the 2 constants

(9 - 6i)(2 - 4i) = (18 - 24) - 48i

Final Answer

-6 - 48i

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How does the Complex Number Operations Calculator work?

Free Complex Number Operations Calculator - Given two numbers in complex number notation, this calculator:
1) Adds (complex number addition), Subtracts (complex number subtraction), Multiplies (complex number multiplication), or Divides (complex number division) any 2 complex numbers in the form a + bi and c + di where i = √-1.
2) Determines the Square Root of a complex number denoted as √a + bi
3) Absolute Value of a Complex Number |a + bi|
4) Conjugate of a complex number a + bi
This calculator has 4 inputs.

What 6 formulas are used for the Complex Number Operations Calculator?

a + bi + (c + di) = (a + c) + (b + d)i
a + bi - (c + di) = (a - c) + (b - d)i
(a * c) + (b * c) + (a * d) + (b * d)
The square root of a complex number a + bi, is denoted as root1 = x + yi and root2 = -x - yi
|a + bi| = sqrt(a2 + b2)
a + bi has a conjugate of a - bi and a - bi has a conjugate of a + bi.

For more math formulas, check out our Formula Dossier

What 8 concepts are covered in the Complex Number Operations Calculator?

absolute valueA positive number representing the distance from 0 on a number lineadditionmath operation involving the sum of elementscomplex numbera number that can be written in the form a + b or a - bicomplex number operationsconjugateA term formed by changing the sign between two terms in a binomial.divisionseparate a number into partsmultiplicationmath operation involving the product of elementssubtractionmath operation involving the difference of elements

Example calculations for the Complex Number Operations Calculator

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