In Exercises 9–20, find each product and write the result in s...

Question

In Exercises 9–20, find each product and write the result in standard form. −3i(7i − 5)

Accepted Answer

Welcome back everyone. In this problem, we want to multiply two I minus nine by negative eight I. And we want to express our answer in standard form for our answer choices A is 16 plus 72. IB is 16 minus 72. IC is 72 plus 16 and I, and the D is 72 minus 16. I now remember we want to express our final answer in standard form for complex numbers and recall that the standard form of a complex number is when it is written in the form A plus B I where A is a real number and B is an imaginary number. So negative eight, I let me put that in red, negative eight, I multiplied by two I minus nine means that we're going to distribute negative eight I across the parentheses. So it would be negative eight, I multiplied by two I which is negative 16 I squared and negative eight I multiplied by negative nine which is positive 72. I no, there's another property of complex numbers that can help us because recall that I squared would be equal to negative one for complex numbers. And just to jog your memory. That's because I equals the square root of negative one. So I squared would be equal to the square root of negative one all squared, which is negative one. So we can apply that property here and rewrite it as negative multiplied by negative one plus 72. I no negative 16 multiplied by negative one is positive 16. So our final answer is 16 plus 72. I and we know it's in standard form because 16 is our real part and 72 is our imaginary part. When we look in our answer choices that would have been answer choice. A thanks a lot for watching everyone. I hope this video helped.

In Exercises 9–20, find each product and write the result in standard form. −3i(7i − 5)

Key Concepts

Imaginary Unit (i)

Multiplication of Complex Numbers

Standard Form of a Complex Number

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