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Mathematics Lab Activity-10 Class XI
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Mathematics Lab Activity-10 Class XI
Chapter - 4 | Complex Numbers
Activity - 10
Objective
To interpret
geometrically the meaning of and its integral powers
Material Required
Card Board, White Chart paper, Pieces of thread, Nail, Pencil etc
Theory
1Complex Number: A number of the form a +ib, where a and b are real numbers, is defined to be a complex number.
Here a is called the real part.
b is called the imaginary part
i is called iota.
⇒ i2
= -1
Other powers of i are as follows
……………………………………………….
………………………………………….
Procedure
1. Take a card board of appropriate size and paste a white chart paper on it .
2. Draw two mutually perpendicular lines XOX’ and YOY’ which cut each
other at point O. as shown in figure 11.1
3. Take a thread of unit length representing the number 1 along OX i.e.
OA = 1
4. Fix one end of the thread to the nail at O and the other end at A as
shown in figure .
Fig 10.1
5. Set free, the other end of the thread at A and rotate it through
angles of 90o, 180o, 270o, and 360o
and mark these points as A1, A2, A3, A4
as shown in figure
Observations
1. In the Argand plane , OA represents = 1
OA1 represents = i = 1 x i
OA2 represents = -1 = 1 x i x i = i2
OA3 represents = – i = 1 x i x i x i = i3
OA4 represents = 1 = 1 x i x i x i x i = i4 = OA
2. From the above explanation we observe
that : Each time , rotation of OA by 90o is equivalent to multiplication by .
3. Therefore, i is referred to as the multiplication factor
for a rotation of 90o.
4. On rotation OA through n- right angles
OAn = 1 x i x i x i x i ……………n times =1 x in
Result
i (iota) is called the multiplication factor for the rotation of 90o.
Applications
This activity can be used to evaluate any integral power of I.
VIVA – VOICE
Q. 1
What is the value of i ?
Ans.
Q. 2. If z =
a +i b, then what is the value of |z| ?
Ans.
Q. 3. What is the value of | i |
Ans. 1
Q. 4. What is
the Argand plane?
Ans. The plane having a
complex number assigned to each of its point is called the complex plane or
Argand plane.
Q. 5. What is
Argand diagram?
Ans. An Argand plane is a plot of complex numbers as points in the complex plane using the x-axis as the real axis and y-axis as the imaginary axis.
THANKS FOR YOUR VISIT
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