Find each product. Write answers in standard form. (3-i)(3+1)(...

Question

Find each product. Write answers in standard form. (3-i)(3+1)(2-6i)

Accepted Answer

Hello everyone we are going to use multiplication to simplify the expression eight minus I times eight plus I times two minus six I so we have multiple Bino meals here and I'm gonna take them two at a time. So I'm going to rewrite the whole thing but the first two I'm going to multiply together are gonna be my eight minus I times my eight plus I I'm not going to touch this third set of parentheses just yet so my eight minus I times my eight plus I I recall that this is the difference of squares. So that means that I can use a special formula where I know that my middle term cancels out. So I square the first term, so eight squared is 64 square my last term I squared and put a minus in between them. So I now have 64 minus I squared times two minus six. I before I go multiply this next set up by no meals. I recall that I squared is the same as negative one. So I'm gonna keep working on this first set of parentheses for another second. So I'm going to replace I squared with negative one and then I notice I have 64 -2. So that's the same as saying 64 plus one. So 65. Now this is down to having 65 times 2 -6. I I need to distribute the 65 into the parentheses, 65 times two is 65, Times six. I is going to be a -390 I And the question wants it to be in standard form because the real part is before the imaginary part, it is currently in standard form. So our solution is 130 -390 I, which is answer choice d. Have a nice day.

Find each product. Write answers in standard form. (3-i)(3+1)(2-6i)

Key Concepts

Complex Numbers and Imaginary Unit

Multiplication of Complex Numbers

Standard Form of a Complex Number

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