Question

How do you multiply \[(6i)( - 4i)\]

Answer 1

Hint: Here in this question, we have to find the product of 2 imaginary numbers. The imaginary number is one form of complex number. So let we multiply 2 imaginary numbers which are different from one another and then we use the arithmetic operation that is multiplication and then we simplify.

Complete step-by-step solution:
A complex number is a combination of the real part and the imaginary part. The imaginary number is represented by “i”. Usually the complex number is defined as \[a \pm bi\].
Now let us consider the two imaginary numbers and they are \[6i\], and \[ - 4i\]
Now we have to multiply the imaginary numbers, to multiply the imaginary numbers we use multiplication. The multiplication is one of the arithmetic operations.
Now we multiply the above 2 imaginary numbers
\[(6i) \cdot ( - 4i)\]
Here dot represents the multiplication. When we multiply 6 into 4 then the product will be 24. The “i” is multiplied twice, so we write in terms of exponent. The multiplication of positive term and the negative term, then product is in the form of negative.
\[ \Rightarrow - 24{i^2}\]
As we know that the value of \[{i^2} = - 1\]. On substituting this we have
\[ \Rightarrow - 24( - 1)\]
On simplification we have
\[ \Rightarrow 24\]
Hence, we have multiplied the two imaginary numbers and obtained the solution which is a real number.

Therefore the correct answer is \[(6i)( - 4i) = 24\]

Note: To multiply we use operation multiplication, multiplication of numbers is different from the multiplication of algebraic expression. In the algebraic expression it involves the both number that is constant and variables. Variables are also multiplied, if the variable is the same then the result will be in the form of exponent.