Question: If z = 2 + 3i, what is the argument of z?
Options:
arctan(3/2)
arctan(2/3)
π/4
0
Correct Answer: arctan(3/2)
Solution:
The argument of z = 2 + 3i is θ = arctan(3/2).
If z = 2 + 3i, what is the argument of z?
Practice Questions
Q1
If z = 2 + 3i, what is the argument of z?
arctan(3/2)
arctan(2/3)
π/4
0
Questions & Step-by-Step Solutions
If z = 2 + 3i, what is the argument of z?
Step 1: Identify the complex number z, which is given as z = 2 + 3i.
Step 2: Recognize that the argument of a complex number is the angle θ formed with the positive x-axis in the complex plane.
Step 3: Use the formula for the argument θ, which is θ = arctan(y/x), where y is the imaginary part and x is the real part of the complex number.
Step 4: In this case, the real part (x) is 2 and the imaginary part (y) is 3.
Step 5: Substitute the values into the formula: θ = arctan(3/2).
Step 6: The result θ = arctan(3/2) gives you the argument of the complex number z.
Complex Numbers – Understanding the representation of complex numbers in the form a + bi, where a is the real part and b is the imaginary part.
Argument of a Complex Number – The argument of a complex number is the angle θ formed with the positive real axis, calculated using the arctangent of the ratio of the imaginary part to the real part.
Polar Coordinates – Converting complex numbers from rectangular form (a + bi) to polar form (r(cos θ + i sin θ)) involves finding the modulus and argument.
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