Concept explainers
Let z = a + bi.
- (a) The modulus of z is r = __________, and an argument of z is an angle θ satisfying tan θ = __________.
- (b) We can express z in polar form as z = __________, where r is the modulus of z and θ is the argument of z.
(a)
The modulus of
Answer to Problem 2E
The modulus of
Explanation of Solution
Given:
The given complex number is
Calculation:
The modulus of complex number
Figure (1)
Formula to find the modulus
Therefore the modulus of
Formula to find the value of
Substitute
Thus the modulus of
(b)
To express: The complex number
Answer to Problem 2E
The polar form of the complex number
Explanation of Solution
Given:
The given complex number is
Calculation:
Formula to find
Substitute
Formula to find
Substitute
Substitute
Thus, the polar form of
Chapter 8 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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