Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
Answer:
[tex](-28) + (-40\, i)[/tex].
Step-by-step explanation:
Expand the expression using the distributive property of multiplication, [tex]X \, (Y + Z) = X\, Y + X\, Z[/tex]:
[tex]\begin{aligned}& (3 + 7\, i)\, (-2 - 2\, i) - (4\, i)\, (5 - 9\, i) \\ =\; & (3 + 7\, i)\, (-2) + (3 + 7\, i)\, (-2\, i) \\ & + (-4\, i)\, (5) + (-4\, i)\, (-9\, i) \\ =\; & (3)\, (-2) + (7\, i)\, (-2) + (3)\, (-2\, i) + (7\, i)\, (-2\, i) \\ & + (-20\, i) + 36\, i^{2} \\ =\; & (-6)\, + (-14\, i) + (-6\, i)+ (-14\, i^{2}) + (-20\, i) + 36\, i^{2} \\ =\; & (-6) + (-40\, i) + 22\, i^{2}\end{aligned}[/tex].
Simplify the expression further using the fact that [tex]i^{2} = (-1)[/tex]:
[tex]\begin{aligned}& (-6) + (-40\, i) + 22\, i^{2} \\ = \; & (-6) + (-40\, i) + (-22) \\ =\; & (-28) + (-40\, i)\end{aligned}[/tex].
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.