Free Printable Advanced Math ni Jervin

1.

Find two complex numbers whose sum is 4 and whose product is 8.

a)

1 ± 2i

b)

2 ± i

c)

1 ± i

d)

2 ± 2i

2.

Simplify i^(39)

a)

1

b)

-i

c)

-1

d)

i

3.

The polar form of (1 + i) is

a)

sqrt. of 2(cos45° + isin45°)

b)

2(cos45° + isin45°)

c)

sqrt. of 2(sin45° + icos45°)

d)

2(sin45° + icos45°)

4.

Express in polar form: -3 - 4i

a)

5e^-i(pi + tan^-1 4/3)

b)

5e^i(pi + tan^-1 4/3)

c)

√5e^i(pi + tan^-1 4/3)

d)

√5e^-i(pi + tan^-1 4/3)

5.

A voltage v = 150 + j180 is applied across an impedance and the current flowing is found to be I = 5 - j4. Determine the resistance.

a)

0.73 ohms

b)

0.77 ohms

c)

0.79 ohms

d)

0.83 ohms

6.

Evaluate the ff: (-1/2 + j/2) raised to the 4th power.

a)

1/8

b)

-1/4

c)

-3/4

d)

1/3

7.

Solve for one value of x in x cubed - 8 = 0.

a)

1 + i sqrt of 3

b)

-3

c)

-2

d)

-1 + i sqrt of 3

8.

Give one indicated root of (-16i) ^1/2 .

a)

2 cis 330°

b)

2 cis 165

c)

2 cis 167.5°

d)

2 cis 67.5°

9.

Give one indicated root of (2 square root of 3 - 2i) ^1/2.

a)

2 cis 330°

b)

2 cis 67.5°

c)

2 cis 165°

d)

2 cis 167.5

10.

If Z1 = 1 - i, Z2 = -2 + 4i, Z3 = √3- 2i, evaluate Z1^2 +2Z1 - 3.

a)

1 + 4i

b)

4 + i

c)

-4 - i

d)

-1 + 4i

11.

If Z1 = 1 - i, Z2 = -2 + 4i, Z3 = sq. rt. of 3 - 2i, evaluate Re{2Z1^3 + 3Z2^2 - 5Z3^2}.

a)

35

b)

35i

c)

-35

d)

-35i

12.

Find all values of z for which e^3z = 1.

a)

kπi

b)

2kπi/3

c)

1/3 kπi

d)

1/8 kπi + 1/2 kπi

13.

Evaluate cosh (ipi/4).

a)

1.414214 L270°

b)

0.707107 L0°

c)

1.414214 L180°

d)

0.707107 L90°

14.

Evaluate tan^2 (j0.78).

a)

0.653

b)

-0. 653

c)

0.426

d)

-0.426

15.

Evaluate L {sin t cos t }.

a)

1/2 (s^2 + 4)

b)

1/(s^2 + 4)

c)

1/(s^2+ 1)

d)

1/2 (s^2 + 1)

16.

Calculate the Laplace transform : L (xe^x).

a)

2/(s - b)^2

b)

b/(s - 2)^2

c)

1/(s - 1)^2

d)

s/(s - 1)^2

17.

Obtain L{t^n}.

a)

n! /s^2 (n - 1)

b)

n! /s^n

c)

n! /s^(n + 1)

d)

(n + 1)! /s^(n + 1)

18.

Evaluate the inverse Laplace transform of 10/s+50

a)

$10e^{-5t}$

b)

$10e^{-t}$

c)

$10e^{-50t}$

d)

$10te^{-5t}$

19.

Given the triangular numbers 1, 3, 6, 10, 15,.. Find the 7th and 8h term of the series.

a)

28 & 36

b)

26 & 24

c)

24 & 26

d)

28 & 34

20.

In a pile of logs, each layer contains one more log than the layer above and the top contains just one log if there are 105 logs in the pile, how many layers are there?

a)

11

b)

12

c)

14

d)

13

21.

Simplify 12 cis 45 deg $\div$ 3 cis 15 deg.

a)

2 + j

b)

sqrt. of 3 + j2

c)

2 sqrt. of 3 + j2

d)

1+ j2

22.

Using power series expansion about 0, find cos x by differentiating from sin x.

a)

1-(x^2/2!) + (x^4/4!) - (x^6/6!) +...

b)

x-(x^2/2!) + (x^4/4!) - (x^6/6!) +...

c)

1-(x^3/3!) + (x^5/5!) - (x^7/7!)+...

d)

x-(x^3/3!) + (x^5/5 !) - (x^7/7!) +...

23.

A periodic function has zero average value over a cycle and its Fourier series consists of only odd cosine terms. What is the symmetry possessed by this function?

a)

even

b)

odd

c)

even quarter

d)

odd quarter

24.

Find the length of the vector (2, 4, 4).

a)

3

b)

4

c)

5

d)

6

25.

The position vectors of point A and B are 2 + i and 3 - 2i respectively. Find an equation for line AB.

a)

3x - y = 5

b)

3x + y = 7

c)

x + 3y = 5

d)

x - 3y = 9

26.

Find a . b if l a l = 26 and | b l = 17 and the angle between them is pi/3.

a)

221

b)

212

c)

383

d)

338

27.

There is a vector v = 7j, another vector u starts from the origin with a magnitude of 5 rotates in the xy plane. Find the maximum magnitude of u x v.

a)

24

b)

70

c)

12

d)

35

28.

Find lu x v| correct to three decimal places where lul = 9, Ivl = 3, $\angle\theta$ = 85 deg.

a)

2.989

b)

31.897

c)

2.353

d)

26.897

29.

the vector which is orthogonal both to 9i + 9j and 9i +9k?

a)

81i +81j - 81k

b)

81i - 81j - 81k

c)

81i - 81j + 81k

d)

81i + 81j + 81k

30.

What is the unit vector orthogonal both to 9i + 9j and 9i + 9k?

a)

$\frac{i}{\sqrt{3}}+\frac{j}{\sqrt{3}}+\frac{k}{\sqrt{3}}$

b)

$\frac{i}{3}+\frac{j}{3}+\frac{k}{3}$

c)

$\frac{i}{\sqrt{3}}-\frac{j}{\sqrt{3}}-\frac{k}{\sqrt{3}}$

d)

$\frac{i}{3}-\frac{j}{3}-\frac{k}{3}$

Advanced Math ni Jervin

Total questions: 30

Worksheet time: 15mins

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