Problem #6: Let u (i , 6i,7),v = (5,-6i, 1 + i),w (6 _ i,6i,3 + 7i)_ComputeExpress your answer in the form a + bi and enter the values a and b (in that order) into ...

Perform each operation. $(i=\sqrt{-1 .})$ Write the result in a+b i \text { form.} $$(7+8 i)-(2-5 i)$$

We're being asked to add to to giving complex numbers. To do this, we have to combine the rial parts and then will combine the imaginary parts. So when we combine the real parts, we're gonna have six plus five plus. And then we're gonna combine the imaginary parts, which are seven I plus three I Well, six plus five is 11 and seven. I plus three. I is positive tonight, so our final answer will be 11.

We're being asked to subtract the two giving complex numbers. To do this, we're first going to subtract the rial parts of our complex numbers. Then we'll subtract the imaginary parts. So we combine those real parts, we're gonna have negative two minus negative seven. And then when we combine, the imaginary parts will have six. I minus I Okay, well, we have to first do. Negative two minus negative seven. Well, that's gonna be positive. Five. Then we have six. I minus I, which is positive. Five I. So our final answer will be five.

If we're given an expression seven plus three I square, we can expand it to seven plus Riyadh times seven plus three i And now we can a fantasy binomial Multiply seven by sun was just 49 plus seven times three I, which is 21 I and then we want to do the same thing to three I So three times seven is 21 I again plus three I times three I, which is nine I squared, is equal to 49 plus, um And since we know that I is equal to square negative one and I been that means I squared must be equal to negative one. So 49 times a plus nine times negative one plus 4 21 plus 21 is 42 I so 49 minus nine is 40 40 plus 42 I is our answer to the problem

Okay, so we went to simplified falling. Well, it's not here that this is the difference of squares. So we can rewrite this as the square root of six well minus ice word tonight. People Just six minus a negative one. And that's equal Teoh a seven.