Question

How do you simplify $ ( - 2i)( - 6i)(4i)? $

Answer 1

Hint: As we know that the above question consists of complex numbers. A complex number is of the form of $ a + ib $ , where $ a,b $ are real numbers and $ i $ represents the imaginary unit. Here the real numbers all the zero i.e. $ (0 - 2i)(3 - 6i)(0 + 4i) $ The term $ i $ is an imaginary number and it is called iota has it has the value of $ \sqrt { - 1} $ . These numbers are not really imaginary. In this question we will multiply this by removing their brackets and keeping the negative signs in mind.

Complete step by step solution:
As per the given question we have $ ( - 2i)( - 6i)(4i) $ .
We will first find the product of the first pair and then w e will multiply the part with the second number. So we have
 $\Rightarrow [( - 2i) \times ( - 6i)](4i) = (12{i^2})(4i) $ .
Since we know that the value of $ {i^2} = - 1 $ ,
we will put this value in the expression and we have,
 $ (12 \times - 1)(4i) = - 12(4i) $ .
We will now multiply the remaining part and it gives: $ - 48i $ .
Hence the required answer is $ - 48i $ .
So, the correct answer is “ $ - 48i $ .”.

Note: We should be careful while solving this kind of questions and we need to be aware of the complex numbers, their properties and the exponential formulas. We should note that the value of $ {i^2} $ is mistakenly taken as $ 1 $ , which is a completely wrong value and it may lead to the wrong answers. We should be careful with complex numbers. So We should also have the idea of exponents as the powers got added when multiplied by the similar variables. In multiplication the signs we should always look for the positive and negative signs of both the numbers as wrong sign can lead to wrong answers.