Solve Q10, 11, 12 explaining detailly each step Transcribed Image Text: COMPLEX NUMBERS

Solve Q10, 11, 12 explaining detailly each step Transcribed Image Text: COMPLEX NUMBERS
a) MCQS:
1. (2+3i)(1 – i) =
2. i =
A. 2 – 2i
B. 2+ 4i C. 5 + i D. – 1+ i
%3D
A. -1 B. -i
С. 1
D. i
3. The imaginary part of i”(2 + V3i) – i(1 – 2i) is: A. V3 –1 B. 0 C. – V3 -1 D. – 4
4. The complex conjugate of (1- i) + (2i – 3)i is:
A. -2 -i B. 3 + 2i
5. (V3 + i) + (1 – V3i) =
C. 3 – 2i D. -1-2i
А. 1
B. -i
C. i D. -1
D. +
2
1.
A. – — L
5
2. 1
i
C. .=+
3
3
1
6.
2+i
2
B.

3 3
5 5
7. If (3 – 2i)z – (7 + 4i) = 0, then z =
A. +
13
26
29
B.+ 2i
29
2
C. 1+ 2i D.

-_re
13
13
-1+iv3
8.
-1-iv3
A. -1- iv3
B. -(2 + iv/3)
C. – (1+ iv3)
D. –(1+ iv3)
|

2
2
9. Given that z
2
–1+3i, z+
A. — B- C– D-+
12
4
В.
18
4
C.-
12
7
11
5
5
3
10. Given that Z1
= 1 -i and z = 2 + i, z;-=
Z.2
4
A.
5
2
4.
B.
5
2
3.
C.
5
2
i
5
8.
+ – i
D.
5
5
11. Given that z and Z are conjugate complex numbers, which cne of the following is not always
true?
A. Re (z) = Re(2) B. Im (z) + Im(2) = 0 C. Re(2) = Im(z) D. (z)
12. The roots cf the equation: z- 6z+ 34 = 0 are
A. -2, 8 B. 6- 10i, 6 + 10i C. -4, 16 D. 3 – 5i, 3 + 5i
13. The quadratic equation with 2 -i as one of its roots is:
A. x+ 5x – 4 0 B. x- 5x + 4= 0 C. x – 4x + 4 = 0
14. p+ 2 is a root of x-x+ 0. The values of p and q are:
(z)
D. x² – 4x – 5 = (0
%3D
17
A. p=
B. p = 1, q = 5
4.
1
17
C. p
15. Given that 5(a + ib) +3 – 2i = 6i, the values of a and b are:
D. p =, G = ”
17
2
A. a = -3, b -8
B. a =
8.
5′
3
C. a =, b = =
3
С.а
a =, b =
8.
5
1
2
1
16. If
(x + iy), the values of x and y are:
|
3-i
1+2i
10
7.
A. x =
B. x = 7, y= 7 C. x 7, y = -7 D. x = -7, y = 7
10
10
17. The complex number -2 + 2i can also be expressed as
A. 2 [cos (-) + i sin (-ĐI
A. 2 cos (-)+ i sin
B. 2 cos () + i sin
+ i sin () D. 2V2 cos (-) + i sin (-|
TT
OS
C. 2v2 fcos () + i sin ( D.2V2 (cos (-) + isin(-)
3T
4
4
4
18. Find the modulus sroument form of the complex number: z = -V3 – i
A. A. 2 [cos +i sm B. z [cos-1sinc 2 cost -i sin
TT
[ca:
COS
COS
+ i sinD. 2 cos-
i sin
5TT
74
IN

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