Question Video: Simplifying the Product of a Complex Number and an Imaginary Number Mathematics

Simplify 𝑖(3 − 5𝑖).

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Video Transcript

Simplify 𝑖 multiplied by three minus five 𝑖.

We will begin this question by distributing the parentheses or expanding the brackets. Multiplying 𝑖 by three gives us three 𝑖, and multiplying 𝑖 by negative five 𝑖 gives us negative five 𝑖 squared. We recall from our knowledge of imaginary numbers that 𝑖 squared is equal to negative one. This means that five 𝑖 squared is equal to five multiplied by negative one. This means that our expression simplifies to three 𝑖 plus five.

Whilst it is not essential, we usually write our complex numbers with the real part first. Writing our expression in the form 𝑎 plus 𝑏𝑖 gives us five plus three 𝑖. The complex number 𝑖 multiplied by three minus five 𝑖 simplifies to five plus three 𝑖.

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