Question

4. Find the values of xanut y much that -3 +isly and x + y + 4 ure conjugates, 5. Find the square root of 7-241 6. What is the real value of '=' for which 31 31 - 2012 + (1 - a)i + 5 in real?

Answer 1

Solh let, Two complex at ib and crid . Then atib is said to be conjugate of crid if - and b= -d. and & 4 Here the complex the complex nas are - tixty kryt we get- * - - - So xy = -4 30, from o we get x² = -3-y we get Pulting thirs in @ (-3-4y = -4 > -3y-y2=-4 y² + 3y4=0 (y + 4) (J-1) 2o. y = 1,-4 when y=1 ch x² = – 3-1 x= tz and when x = -3+ 4 y=-4 na 1 E = Il So, the values of x and y (22, 1) (-22, 1), (1-4), (-1,4)

5. Let atib is the I-24 i root of square so Carib) ² = 7-24 à +2.ailb+ (b) 2 = 7-24 i a 22-6² + zabi +zabi - 7-24 i So a_62 = 7 0 zab = -24 ☺ e from 0, we get, a = 6 +7 Now, from ③ - 26 = 144 + (6 + 7) 6² = 144 (from, a=6²47) 64 + 76² = 144 64 + 76²_144=0 then Let, = u u +74-144=0 U u²+bu-gu-144 = 0 - (M+16) (4-9)=0 u=-169 Thus, b²= -l or 62-9 b= +40 or b=+3. and bare since, real no. so b & +45 a Thus b = 13

so a² = 987 > a2 = 16 a= + 4 since, gab = -24, so, both the sign and b can not be the came. Soo, Of a=4,6=-3 a=-4, b = 3 Thus, the square roofs of 7-24e area (4-3i) and (-4+32) fee

6 3.313 + (1-a) i ts 31:3 (-2) + (1-a) i 45 = 9.(-22) ti-aits 9 +5+ (-a) 14+ (1-a) i . This will be a real no. if the imaginary past i zero, to T a=1. Thus, for for a=1 31:31 3+ (1-a) i 45 is real