Assignment:
Q1. Find the absolute value of the following complex number:
a. z = 2 + 5i
Q2. Choose the rectangular coordinates for the following polar coordinate:
a. (-6, 3π/2 )
Q3. Determine the rectangular form of the complex number:
z = 8 (cosπ/2 = i sinπ/2 )
Q4. Find the polar form of the following complex number:
a. z = 7 ( cos3π/2 + i sin3π/2 )
Q5. When plotted on the rectangular coordinate system in which quadrant would the following point be located for this polar coordinate?
a. ( -2 , 2π/3 )
b. ( -3, π/4 )
Q6. Find the power of the following complex number:
z = ( √2 - i )4
Q7. Find the value of the given complex number:
i5
Q8. Choose the polar coordinates for the following rectangular coordinate:
( -1, -√3 )
Q9. The following polar coordinates are multiple representations of the same point, True or False?
( -5, 7π/4 ) ( -5, 5π/4 )
Q10. Find the polar form of the following expression:
3√2 - 3√2i
Q11. Write each complex number in rectangular form. If necessary round to the nearest tenth.
4( cos5π/6 + i sin 5π/6)
Q12. Use DeMoirvre’s Theorem to find the indicated power of the complex number. Write answer in rectangular form.
[1/2 (cos π/10 + i sin π/10)]5
Provide complete and step by step solution for the question and show calculations and use formulas.