(a)
To sketch: The point
(a)
Explanation of Solution
The
The real part of the number is 1 and the imaginary part is
The graph of the complex number is,
Figure (1)
The above graph shows the point
(b)
The polar form of the given complex number.
(b)
Answer to Problem 4T
The polar form of the complex number
Explanation of Solution
Given:
The complex number is
Calculation:
The modulus r of the complex number
Substitute 1 for a and
The modulus of the complex number is 2.
The argument
Substitute 1 for a and
The argument
The given complex number is
In general the polar form of the complex number
The value of r is 2 and the value of
Substitute 2 for r and
Thus, the polar form of the complex number
(c)
The value of
(c)
Answer to Problem 4T
The value of
Explanation of Solution
Given:
The below number is a complex number with power 9.
Formula used:
De Moivre’s Theorem.
Where,
The number
Calculation:
From part (b) the polar form of the complex number
Substitute 9 for
Thus, the value of
Chapter 8 Solutions
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