# JMAP Worksheets by Topic RADICALS Complex Numbers

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```					Regents Exam Questions by Topic                                                       Page 1
RADICALS: Multiplication and Division of Complex Numbers
www.jmap.org                                       Name: __________________________________

1      The expression i 0  i1  i 2  i 3  i 4 is equal to
(1) 1         (3) i
060410b   (2) -1        (b)-i

2                          i 16
The expression           is equivalent to
i3
010518b
(1) 1              (3) i
(2) -1             (4) –i

3      What is the multiplicative inverse of 3i?
1
060614b   (1) -3i       (3)
3
i
(2) -3        (4) 
3

4      The expression 3i (2i 2  5i ) is equivalent to
(1) 15  6i             (3) 15  5i
(2) 15  5i             (4) 1  0i
080702b

5      The complex number c  di is equal to (2  i ) 2 . What is the value of c?
080621b
6      The expression ( 1  i ) 3 is equivalent to
(1) –3i       (3) –1 – i
010219b
(2) –2 – 2i   (4) 2 + 2i

7      Show that the product of a + bi and its conjugate is a real number.

080122b
8      In an electrical circuit, the voltage, E, in volts, the current, I, in amps, and the
opposition to the flow of current, called impedance, Z, in ohms, are related by
010325b   the equation E = IZ. A circuit has a current of (3 + i) amps and an impedance of
(–2 + i) ohms. Determine the voltage in a + bi form.

9      The relationship between voltage, E, current, I, and resistance, Z, is given by
the equation E = IZ. If a circuit has a current I = 3 + 2i and a resistance Z = 2 –
060304b   i, what is the voltage of this circuit?
(1) 8 + i       (3) 4 + i
(2) 8 + 7i      (4) 4 – i
Regents Exam Questions by Topic                                                       Page 2
RADICALS: Multiplication and Division of Complex Numbers
www.jmap.org                                       Name: __________________________________

10       The expression
10
is equivalent to
3i
010811b
15  5 i
(1) 3i               (3)
4
5
(2) 3i               (4)
4

11                       2i
The expression        is equivalent to
3i
060513b
6  5i         7  5i
(1)            (3)
8             10
6i            7i
(2)            (4)
8              10

12       Impedance measures the opposition of an electrical circuit to the flow of
electricity. The total impedance in a particular circuit is given by the formula
060509b           ZZ
ZT  1 2 . What is the total impedance of a circuit, ZT , if Z1  1  2i and
Z1  Z2
Z2  1  2i ?
5
(1) 1          (3)
2
3
(2) 0          (4) 
2

13                                      20
Expressed in simplest form,        is equivalent to
5
080905b
(1) -2i        (3)    2i
2i
(2) 2i         (4)
5

14                         50
The expression        is equivalent to
080816b
2
(1) -5i        (3) 5i
(2) -5         (4) 5

15       What is the product of 5  36 , and 1  49 , expressed in simplest a + bi
form?
080314b
(1) –37 + 41i        (3) 47 + 41i
(2) 5 – 71i          (4) 47 – 29i

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