For Exercises 31-42, given complex numbers z 1 and z 2 , a. Find z 1 z 2 and write the product in polar form. b. Find z 1 z 2 and write the quotient in polar form. (See Example 5-6) z 1 = 3 cos 7 π 4 + i sin 7 π 4 , z 2 = 6 cos 7 π 12 + i sin 7 π 12
For Exercises 31-42, given complex numbers z 1 and z 2 , a. Find z 1 z 2 and write the product in polar form. b. Find z 1 z 2 and write the quotient in polar form. (See Example 5-6) z 1 = 3 cos 7 π 4 + i sin 7 π 4 , z 2 = 6 cos 7 π 12 + i sin 7 π 12
Solution Summary: The author calculates the following complex numbers: z_1cdot2 in polar form is 18left.
For Exercises 31-42, given complex numbers
z
1
and
z
2
,
a. Find
z
1
z
2
and write the product in polar form.
b. Find
z
1
z
2
and write the quotient in polar form. (See Example 5-6)
z
1
=
3
cos
7
π
4
+
i
sin
7
π
4
,
z
2
=
6
cos
7
π
12
+
i
sin
7
π
12
Combination of a real number and an imaginary number. They are numbers of the form a + b , where a and b are real numbers and i is an imaginary unit. Complex numbers are an extended idea of one-dimensional number line to two-dimensional complex plane.
rmine the immediate settlement for points A and B shown in
figure below knowing that Aq,-200kN/m², E-20000kN/m², u=0.5, Depth
of foundation (DF-0), thickness of layer below footing (H)=20m.
4m
B
2m
2m
A
2m
+
2m
4m
sy = f(x)
+
+
+
+
+
+
+
+
+
X
3
4
5
7
8
9
The function of shown in the figure is continuous on the closed interval [0, 9] and differentiable on the open
interval (0, 9). Which of the following points satisfies conclusions of both the Intermediate Value Theorem
and the Mean Value Theorem for f on the closed interval [0, 9] ?
(A
A
B
B
C
D
=
Q6 What will be the allowable bearing capacity of sand having p = 37° and ydry
19 kN/m³ for (i) 1.5 m strip foundation (ii) 1.5 m x 1.5 m square footing and
(iii)1.5m x 2m rectangular footing. The footings are placed at a depth of 1.5 m
below ground level. Assume F, = 2.5. Use Terzaghi's equations.
0
Ne
Na
Ny
35 57.8 41.4 42.4
40 95.7 81.3 100.4
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
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