Math Problem Statement
Express Z=-2+2i3^1/2
Solution
To express the complex number in polar form, we need to find its magnitude and angle .
Step 1: Calculate the magnitude
The magnitude of a complex number is given by: For , where and :
Step 2: Calculate the angle
The angle (also known as the argument) is found using: For : Since the real part is negative and the imaginary part is positive, the complex number is in the second quadrant. Therefore, we need to add to the principal angle found:
Step 3: Write the polar form
Thus, the polar form of is:
Final Answer:
or simply,
Would you like more details or have any questions?
Here are five related questions:
- How would you convert a complex number from polar form back to rectangular form?
- What is the significance of the argument in the polar form of a complex number?
- How do you find the polar form of a complex number if it lies in the third or fourth quadrant?
- What is the geometric interpretation of the magnitude and angle in polar form?
- How would the polar form change if the complex number was multiplied by a scalar?
Tip: When determining the angle in polar form, always consider the correct quadrant of the complex number to get the proper direction of the angle.
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Math Problem Analysis
Mathematical Concepts
Complex Numbers
Polar Form
Trigonometry
Formulas
Magnitude of a Complex Number
Angle of a Complex Number in Polar Form
Theorems
Argument (Angle) of a Complex Number
Suitable Grade Level
Advanced High School