question \ntype the correct answer in each box. use numerals instead of words.\nfind the values of x and y…

question \ntype the correct answer in each box. use numerals instead of words.\nfind the values of x and y in these equations.\n$(x + yi) + (4 + 6i) = 7 - 2i$(equation a)\n$(x + yi) - (-8 + 11i) = 5 + 9i$(equation b)\nin equation a, x = \nand y = \n.\nin equation b, x = \nand y = \n.

question \ntype the correct answer in each box. use numerals instead of words.\nfind the values of x and y in these equations.\n$(x + yi) + (4 + 6i) = 7 - 2i$(equation a)\n$(x + yi) - (-8 + 11i) = 5 + 9i$(equation b)\nin equation a, x = \nand y = \n.\nin equation b, x = \nand y = \n.

Answer

Equation A:

Explanation:

Step1: Start with the equation

We have the equation ((x + yi) + (4 + 6i) = 7 - 2i).

Step2: Combine like terms

Combine the real parts and the imaginary parts separately. So, ((x + 4) + (y + 6)i = 7 - 2i).

Step3: Equate real and imaginary parts

For the real parts: (x + 4 = 7). Solving for (x), we subtract 4 from both sides: (x = 7 - 4 = 3). For the imaginary parts: (y + 6 = -2). Solving for (y), we subtract 6 from both sides: (y = -2 - 6 = -8).

Equation B:

Explanation:

Step1: Start with the equation

We have the equation ((x + yi) - (-8 + 11i) = 5 + 9i).

Step2: Simplify the left side

Distribute the negative sign: ((x + yi) + 8 - 11i = 5 + 9i). Then combine like terms: ((x + 8) + (y - 11)i = 5 + 9i).

Step3: Equate real and imaginary parts

For the real parts: (x + 8 = 5). Solving for (x), we subtract 8 from both sides: (x = 5 - 8 = -3). For the imaginary parts: (y - 11 = 9). Solving for (y), we add 11 to both sides: (y = 9 + 11 = 20).

Answer:

In equation A, (x = 3) and (y = -8). In equation B, (x = -3) and (y = 20).