ข้อสอบ A-Level คณิตประยุกต์ 1 ปี 2560 (วิชาสามัญเก่า)

ข้อ 11

ถ้า straight z เป็นจำนวนเชิงซ้อน ซึ่งสอดคล้องกับสมการ straight z plus open vertical bar fraction numerator top enclose straight z minus 1 over denominator straight z minus 1 end fraction close vertical bar equals negative 3 plus 2 straight i  แล้ว open vertical bar straight z close vertical bar มีค่าเท่ากับข้อใดต่อไปนี้

รีวิว - เสียงตอบรับจากผู้เรียน

เฉลยข้อสอบ

สมมติให้ z = a + bi และ begin mathsize 14px style straight z with bar on top end style = a - bi


begin mathsize 12px style จากโจทย ์ space space space space space space space space space space space z plus open vertical bar fraction numerator z with bar on top minus 1 over denominator z minus 1 end fraction close vertical bar space equals space minus 3 plus 2 straight i

จะได ้ space space space space space space left parenthesis straight a plus bi right parenthesis plus open vertical bar fraction numerator left parenthesis straight a minus bi right parenthesis space minus 1 over denominator left parenthesis straight a plus bi right parenthesis minus 1 end fraction close vertical bar equals negative 3 plus 2 straight i
space space space left parenthesis straight a plus bi right parenthesis plus fraction numerator square root of left parenthesis straight a minus 1 right parenthesis squared plus left parenthesis negative straight b right parenthesis squared end root over denominator square root of left parenthesis straight a minus 1 right parenthesis squared plus left parenthesis straight b right parenthesis squared end root end fraction equals negative 3 plus 2 straight i
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space left parenthesis straight a plus bi right parenthesis space plus 1 space equals space minus 3 plus 2 straight i
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space straight a plus bi space equals space minus 4 plus 2 straight i
space space space space space space space space space space space space space space space space ด ั งน ั้ น space space space space space space space space space space space space space space space space space space space space space space space space space space space z space equals space minus 4 plus 2 straight i end style

begin mathsize 12px style จากส ู ตร space space space space space space space space space space space space space S subscript n space equals space n over 2 open square brackets 2 a subscript 1 plus open parentheses n minus 1 close parentheses d close square brackets
space space space space space space space space space space space space space space space space space space space space space space space space space space space S subscript 9 space equals space 9 over 2 open square brackets 2 a subscript 1 plus 8 d close square brackets
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space fraction numerator 9 over denominator up diagonal strike 2 end fraction open parentheses up diagonal strike 2 close parentheses open square brackets a subscript 1 plus 4 d close square brackets
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 9 open parentheses a subscript 1 plus 4 d close parentheses space space space space space space semicolon space จาก space box enclose 1 space a subscript 1 plus 4 d equals 15
space space space space space space space space space space space space space space space space space space space space space space space space space space space space S subscript 9 space equals space 9 open parentheses 15 close parentheses
space space space space space space space space space space space space space space space space space space space space space space space space space space space space S subscript 9 space equals space 135 end style

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