Complex numbers - practice problemsDirection: Solve each problem carefully and show your solution in each item.
Number of problems found: 55
- Complex expr with fractions
Find 1½ of 16 ÷2⅓+(2¼ of ⅑). Use correct order of operations. The order is PEMDAS: Parentheses, Exponents, Multiplication, and Division (from left to right), Addition and Subtraction (from left to right).
- Turtles 2
A box turtle hibernates in the sand at 11 5/8 ft. A spotted turtle hibernates at 11 16/25 feet. Which turtle is deeper? Write the answer as number 1 or 2.
- Function 59513
Expand the function f (z) into the Laurent series at point z0 for the given annulus f (z) = 1 / ((z-2) * (z-3)) a) z0 = 2, 0 3
- Mistake in expression
While attempting to multiply the expression (2 - 5i)(5 + 2i), a student made a mistake. (2 - 5i)(5 + 2i) = 10 + 4i - 25i - 10i2 = 10 + 4(-1) - 25(-1) - 10(1) = 10 - 4 + 25 - 10 = 21 Complete the explanation and correct the error. Hint: The student incorre
- Suppose 5
Suppose z5=2+3i and z6=6+9i are complex numbers and 3 z5 + 7 z6= m+in. What is the value of m and n?
- Complex plane mapping
Show that the mapping w = z +c/z, where z = x+iy, w = u+iv, and c is a real number, maps the circle |z| = 1 in the z-plane into an ellipse in the (u, v) plane.
- Two grandmothers
Two grandmothers went to sell eggs at the market, and they had 100. When they sold all the eggs, they made the same money. The first grandmother says to the second: "If I sold my eggs for your price, I would earn 15 crowns. " The other grandmother replies
- Cis notation
Evaluate multiplication of two complex numbers in cis notation: (6 cis 120°)(4 cis 30°) Write the result in cis and Re-Im notation.
- Imaginary numbers
Find two imaginary numbers whose sum is a real number. How are the two imaginary numbers related? What is their sum?
- ReIm notation
Let z = 6 + 5i and w = 3 - i. Compute the following and express your answer in a + bi form. w + 3z
- Let z 3
Let z = -5 + i and w = 4 - 2i. Compute z - w and write your final answer in a + bi form. x = z - w
- The expression 2
The expression (3+i)(1+2i) can be written in the form a+bi, where a and b are integers. What are the values of a and b?
- Evaluate 18
Evaluate the expression (-4-7i)-(-6-9i) and write the result in the form a+bi (Real + i* Imaginary).
- An Argand diagram
Find the sum z1+z2 and difference z1-z2 and z2-z1 of z1=5+2i and z2=2+3i by an Argand diagram.
- Let z1=x1+y1i
Let z1=x1+y1i and z2=x2+y2i Find: a = Im (z1z2) b = Re (z1/z2)
- Modulus and argument
Find the mod z and argument z if z=i
- Determine 3888
Determine the sum of the three-third roots of the number 64.
- Difference 4102
Determine the difference between two complex numbers: 3i²-3i4
- Determine 4083
Determine the sum of complex numbers: 2i² + 2i4
- Complex number coordinates
Which coordinates show the location of -2+3i
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