## Complex Numbers

Posted on: April 19, 2018, by :  acca online tutoring, online tutoring, acca online academy, statistics tutor, stats tutor, statistics tuition, statistics teacher, acca stats tutor,

COMPLEX NUMBERS

COMPLEX NUMBERS PAST PAPERS KARACHI BOARD (XI)

By Sir Farhan Jaffri

Real Complex Numbers

2008.

Q.1. (a) (ii). Express X2 + y2=9 in terms of conjugate co-ordinates

(iii) If Z1= 1 +I and Z2=3+2i, evaluate |Z1 – 4Z2|.

(b) (i): Find the real and imaginary parts of i(3+2i).

(ii) Find the multiplicative inverse of the complex no, (3,5)

Q.1 (a)(ii) If Z1= 1 +I and Z2=3+2i, evaluate |5Z1 – 4Z2|

(iii) Solve the complex equations (x,y).(2,3)=(-4,7)

(b) Separate the following into real and imaginary parts

(1+2i)/(3-4i) + 2/5

2006.

Q.1. (b) Show that (a,b).(a/a2+b2, -b/a2+b2) = (1,0)

Q.1. ( c ) If z=(x,y), then show that Z.Z’ =|Z|2

2005.

Q.1. (a) (ii). Solve the complex equation, (x + 2yi)2 = xi

2004.

Q.1. (a) (ii) If Z1 and Z2  are complex numbers, verify that | Z1. Z2|=| Z1|| Z2|

(iii) Solve the complex equations (x,y).(2,3)=(-5,8)

2003.

Q.1. (a)(ii). If Z1= 1 +I and Z2=3+2i, evaluate |5Z1 – 4Z2|

(iii) Separate (7-5i)/(4+3i) into real and imaginary parts.

(iv) Find the additive and multiplicative inverse of (3,-4)

2002.

Q.1. (a) (ii) Find the multiplicative inverse of (√3+i)/( √3-i), separating the real and imaginary parts.

(iii) Solve the complex equations (x,y).(2,3)=(5,8)

2001.

Q.1. (a) (ii) Define modulus and the conjugate of complex numbers Z= x – iy

(iii) If Z= (1+i)/(1-i), then show that Z.Z’=|Z|2 verify that

(1+3i)/(3-5i) + -4/17 = -4/17 + 7i/17

2000.

Q.1. (a) (ii) Separate into real and imaginary parts (1+2i)/(2-i) and hence find |(1+2i)/(2-i)|.

(iii) By using the definition of multiplicative inverse of two ordered pairs, find the multiplicative inverse of (5,2) and solve the equation (2,3).(x,y)=(-4,7)

1999.

Q.1.(a)(ii) Divide 4+I by 3-4i.

(iii)Prove that (3/25, -4/25) is a multiplicative inverse of (3,4)

(iv) Multiply (-3,5) by (2,1)

1998.

Q.1.(a)(ii) Solve the complex equation (x + 2yi)2 = xi

(iii) Find the additive and multiplicative inverse of (2-3i).

(iv) Is there a complex number whose additive and multiplicative inverse are equal?

1997.

Q.1.(a)(ii) If Z1 and Z2  are complex numbers, verify that | Z1. Z2|=| Z1|| Z2|

1996.

Q.1. (b)(iv). The multiplicative identity in C is ___________.

Q.1. © What is the imaginary part of [(2+7i)’]2.

1995.

Q.1.(a) Show that (1-i)4 is a real number.

Q.1. (b) Find the additive and multiplicative inverse of (1,-3)

1994.

Q.1.(b) If Z1 = 1-I and Z2=3+2i evaluate (i) [(Z1)’]2 (ii) Z1/Z2

1993.

Q.1.(a) If Z1 and Z2  are complex numbers, verify that | Z1. Z2|=| Z1|| Z2|

1992.

Q.1. (a) (ii) Simplify (x,3y).(2x-y)

Q.1. (a) (iii) show that Z = 1±i, satisfies the equation Z2-2Z+2=0

1991.

Q.1.(a) (ii)  Express X2+Y2=9 in terms of conjugate co-ordinates

Q.1. (b)(i) Solve the complex equation (X + 3i)2 = 2yi