I Vay CO hai can bac hai (dang dai so) cu aw la:
Giai tac6 nghi fm la:
Dat z = X + yi
a) |2i-2z I = | 2 z - l I <::>4 x 2-4(y + 1)^ = (2x- 1)^ + 4y2
» 4x2 + 4y2 + 8y + 4 = 4x2 + 4y2 - 4x + 1 <=> 4x + 8y + 3 = 0
Tap hgp cac diem bieu dien la duong thang c6 phuang trinh: 4x + By + 3 = 0 b) |z + l + z i | < 0 < » iz + l - 2 i | = 0 o ix + l + ( y - 2 ) i | = 0 b) |z + l + z i | < 0 < » iz + l - 2 i | = 0 o ix + l + ( y - 2 ) i | = 0
(x + 1)2 + (y - 2)2 = 0 <=> x = - 1 , y = 2 Tap hgp la diem M ( - l ; 2) Tap hgp la diem M ( - l ; 2)
c) I X - 2 + yi 12 + I X + 2 + yi 12 = 26 o (x - 2)2 + y2 + (x + 2)2 + y2 = 26
<=> x2 + y2 = 9.
Tap hgp cac diem bieu dien la duang tron tarn O ban kinh R = 3.
r i u f i ^ n«» A ^ * ^ - ^
d) z + i = !<=> |z + i | = | z - 3 i z - 3 i z - 3 i
« x2 + (y + 1)2 = x2 + (y - 3)2 c:> y = 1
Tap hgp cac diem bieu dien la duang thing y = 1 z + w = 3(1 + i) z + w = 3(1 + i)
Bai 13: Tim hai so phuc z va w thoa man: Giai Giai
+ =-9 + 9i
z3 + = -9 + 9i •» (z + w)^ - 3(z + w) zw = -9(1 + i) 3(l + i ) ^ + ( l - i ) 3(l + i ) ^ + ( l - i ) Hay z + w = 3(1 + i) =^ zw = ^^-7^ = 5i Do do: z va w la nghiem cua phuang trinh:
z2 = 3(1 + i)z + 5i = 0. z = 2 + i z = 2 + i
Giai ta c6 nghif m la:
Giai ta c6 nghif m la:
= 3 + 4i = (2 + i)2. Vay c6 hai can bac hai cua zi la: 2 + i va 2 - i
â-b^=-3V2
3V2 .N/3
z, = + 1 — . Giai he
2 2 2 2ab =
Bai 15:
a) Tim modun cua so phuc z = 4 - 3i + (1 - i)^ b) Viet dang lugng giac cua so phuc z = 1 - \/3 i b) Viet dang lugng giac cua so phuc z = 1 - \/3 i
Giai
a) z = 4 - 3i + (1 - i)^ = 4 - 3i - 2 - 2i = 2 - 5i
= ^f29
b) z = 1 - V3 i = 2 1 s . 1
2 2 = 2 cos + ism . 3
Bai 16: Giai phuang trinh: z^ + (1 - 2i)z2 + (1 - i)z - 2i = 0 biet rkng phuang trin