h h h h h h h h
Ch.h2 PolynomialhandhRationalhFunctions
2.1 ComplexhNumbers
1 Addh andh Subtracth Complexh Numbers
MULTIPLEh CHOICE.h Chooseh theh oneh alternativeh thath besth completesh theh statementh orh answersh theh question.
Addh orh subtracth ash indicatedh andh writeh theh resulthinh standardh form.
1)h (5h -h6i)h+h(9h+h9i)
A)h 14h+h3i B)h 14h-h3i C)h -4h+h15i D)h -14h-h3i
2)h(9h+h5i)h-h(-
8h+hi)hA)h 17h+h B)h 17h-h4i C)h 1h+h6i D)h -17h-h4i
4i
3)h 8ih+h(-7h -hi)
A)h -7h+h7i B)h -7h+h9i C)h 7h -h7i D)h 7h -h9i
4)h5ih-h(-5h-hi)
A)h 5h+h6i B)h -5h-h6i C)h 5h -h4i D)h -5h +h4i
5)h (-7h +h6i)h-h9
A)h -16h+h6i B)h 16h-h6i C)h 2h+h6i D)h 2h-h6i
6)h-2h-h(-h2h-h8i)h-h(-h2h-h6i)
A)h2h+h14i B)h 2h-h14i C)h 4h-h14i D)h 4h+h14i
7)h (4h-h3i)h+h(1h-h6i)h+h(4h+h5i)
A)h 9h-h4i B)h7h+h8i C)h 1h-h14i D)h 5h-h9i
2 Multiplyh Complexh Numbers
MULTIPLEh CHOICE.h Chooseh theh oneh alternativeh thath besth completesh theh statementh orh answersh theh question.
Findh theh producth andh writeh theh resulth inh standardh form.
1)h -5i(3ih-h9)
A)h15h+h45i B)h -15h+h45i C)h 45ih-h15i2 D)h 45ih+h15i2
2)h 7i(-3ih +h6)
A)h21h+h42i B)h -21h+h42i C)h 42ih-h21i2 D)h 42ih+h21i2
3)h(9h+h8i)(5h-h5i)
A)h 85h-h5i B)h85h+h5i C)h5h+h85i D)h -40i2h -h5ih+h45
4)h (-6h+h9i)(5h+hi)
A)h -39h+h39i B)h -21h+h39i C)h -39h-h51i D)h -21h-h51i
5)h (8h-h6i)(-5h-h3i)
A)h -58h+h6i B)h -58h-h54i C)h -22h+h6i D)h -22h-h54i
6)h (9h +h3i)(9h -h3i)
A)h 90 B)h 81h-h9i2 C)h 72 D)h 81h-h9i
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h h h h h h h h
7)h (-4h +hi)(-4h -hi)
A)h 17 B)h -4 C)h 16 D)h -15
8)h (4h +h9i)2
A)h -65h+h72i B)h 97h+h72i C)h -65 D)h 16h+h72ih+h81i2
Performh theh indicatedh operationsh andh writeh theh resulth inh standardh form.
9)h (7h +h8i)(3h -hi)h-h(1h -hi)(1h +hi)
A)h27h+h17i B)h31h+h17i C)h29h+h17i D)h 27h+h31i
10)h (2h +hi)2h -h(6h -hi)2
A)h -32h+h16i B)h 32h+h16i C)h -48 D)h -32h-h16i
Complexh numbersh areh usedh inh electronicsh toh describeh theh currenth inh anh electrich circuit.h Ohm'sh lawh relatesh theh curre
nthinh ah circuit,h I,hinhamperes,h theh voltageh ofh theh circuit,h E,h inh volts,h andh theh resistanceh ofhtheh circuit,h R,h inhohms,hbyh t
hehformulahEh =hIR.hSolvehthehproblemhusinghthishformula.
11) Findh E,h theh voltageh ofh ah circuit,h ifh Ih =h(8h +h9i)h amperesh andh Rh =h(4h +h 7i)h ohms.
A)h (-31h+h92i)hvolts B)h (-31h-h92i)hvolts C)h (92h-h31i)hvolts D)h (92h+h31i)hvolts
12) Findh E,h theh voltageh ofh ah circuit,h ifh Ih =h(18h +h i)h amperesh andh Rh =h(2h +h3i)h ohms.
A)h (33h+h56i)hvolts B)h (33h-h56i)hvolts C)h (-18h +h56i)h volts D)h (-18h-h56i)hvolts
3 Divideh Complexh Numbers
MULTIPLEh CHOICE.h Chooseh theh oneh alternativeh thath besth completesh theh statementh orh answersh theh question.
Divideh andh expressh theh resulth inh standardh form.
7
1)
8h-hi
56h h 7h h 56h h 7h 8h h 1h 8h h 1h
+ i - i + i - i
h h
A)h B) C) D)
65 65 65 65 9 9 9 9
8
2)
2h+hi
16h h 8h 16h h 8h 16h h 8h 16h h 8h
- i + i + i - i
h h h
A)h B) C) D)
5 5 5 5 3 3 3 3
h 10ih
3)
3h+hi
A)h1h+h3i B)h -1h+h3i C)h 1h+h10i D)h 1h-h3i
h 4ihh
4)
3h+hi
2h 6h 2h 6h 1h 3h 2h 6h
A)h h+h i B)h -h +h ih
C)h +h ih
D)h -h i
h
5 5 5 5 2 2 5 5
hhhh 2ih
5)
1h +h7i
7 + h 1h i B)h
1 7h
+h i C)h -h
7 1h
+h i D)h -h
1
-h
7h
i
A)
25 25 25 25 24 24 24 24
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h h h h h h h h
h 4h+h5i
6)
5h-h4i
A) i B)h -i C)h 1 D)h -1
h 5h -h4i
7)
8h +h6i
4h h 31h 2h h 31h 32h h 1h 16h h 31h
- - + i -
h h h h
A) i B) i C) D) i
25 50 7 28 25 25 7 28
h 3h+h4i
8)
9h-h3i
h 1h h 1h 1h h 1h 13h h 9h 13h h 1h
A) + i + i - i + i
h h h
B) C) D)
6 2 72 24 2 2 24 24
h 2h+h3i
9)
5h +h2i
4
h 16h h 11h 16h h 11h 4 -h 19hi D)h 11h
+ i + i +h i
h
A) B) C)h
29 29 21 21 29 29 21 21
h 5h +h8i
10)
4h +h2i
h 9h h 11h 3h 11h 2h 21h 1h 11h
A) + i B)h +h
h
i C)h h
-h i D)h +h
h i
5 10 2 12 5 5 3 12
h 4h -h3i
11)
5h-h3i
h 29h h 3h 29h 3h 11h 27h 11h 3h
A) - i B)h -h
h
i C)h +h
h
i D)h -h i
h
34 34 16 16 34 34 16 16
4 Performh Operationsh withh Squareh Rootsh ofh Negativeh Numbers
MULTIPLEh CHOICE.h Chooseh theh oneh alternativeh thath besth completesh theh statementh orh answersh theh question.
Performh theh indicatedh operationsh andh writeh theh resulth inh standardh form.
1) -16 + -81
A)h 13i B)h -13i C)h 36i D)h -13
2)h -3h-h -121
A)h i(h 3h-h11) B)h 3ih-h11 C)h 3ih-h11i D)hi(h 3h+h11)
3)h 3h -64h+h4h -49
A)h 52i B)h -52 C)h 52 D)h -52i
4)h 2h -32h+h5h -50
A)h 33ih 2 B)h -33h 2 C)h 33h 2 D)h -33ih 2
5)h (-8h-h -49)2
A)h 15h +h112i B)h113h+h112i C)h 64h+h49i D)h 64h-h49i
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h h h h h h h h
6)h(-6h+h -100)2
A)h -64h-h120i B)h136h+h120i C)h 36h+h100i D)h 36h-h100i
7)h (h 6h-h -h64)( 6 +h -h64)
A)h 70 B)h -58 C)h 6h -h64i D)h 6h -h8i
8)h(3h+h -3)h(3h+h -2)
A)h (9h-h 6h)+h(3h 2h+h3hhh 3)i B)h (9h +h 6h )-h15i
C)h 3h-h6h 6i D)h 15h+h36i
-2h+h -12
9)h
2
A)h -1h+hi 3 B) -1h -hi 3 C) 1h +hi 3 D) -1h+hi 2
-42h-h -252
10)h
6
A) -7h-hi 7 B) -7h +h i 7 C) 7h +hi 7 D)h -7h-hi 6
11)h -16(5h-h -9)
A)h 12h+h20i B)h 20ih-h12 C)h 20ih-h12i2 D)h 20ih+h12i2
12)h (h -9)(h -64)
A)h -24 B)h 24i2 C)h 24 D)h -24i
5 Solveh Quadratich Equationsh withh Complexh Imaginaryh Solutions
MULTIPLEh CHOICE.h Chooseh theh oneh alternativeh thath besth completesh theh statementh orh answersh theh question.
Solveh theh quadratich equationh usingh theh quadratich formula.h Expressh theh solutionh inh standardh form.
1)h x2h +h xh +h 2h =h0
A)h - B)hh
h 1h
±h i
h 7
C)
h 1h
±h
hhh 7
D)h -
1
h h
±h
hhh 7
h 1h h 7
±h i
2 2 2 2 2 2 2 2
2)h x2h -h 12xh +h 40h =h0
A)h {6h±h2i} B)h {6h±h4i} C)h {6h+h2i} D)h {4,h 8}
3)h 8x2h +h3xh +h3h =h0
h 3h h 87 3h 87 3h 8 3h 87
A)h - ±h i B)h - ±h ±h i ±
h hhh hh h hh h h
C)hh D)hh
7
16 16 16 16 16 16 16 16
4)h 16x2h -h 5xh +h 1h =h0
hh 5h h 39 5h h 39 5h hhh 39 5h h h 39
A)hh ±h i B)h -
h
±h i C)h -
h
±h D)hh
hh
±
32 32 32 32 32 32 32 32
5)h 5x2h =h-9xh -h7
h 9h h 59 9h 59 9h 5 9h 59
A)h - ±h i B)h -
h
±h
hhh
C)hh
hh
±h i
h
D)hh
hh
±
h h
9
10 10 10 10 10 10 10 10
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