# Complex numbers - practice problems

Direction: Solve each problem carefully and show your solution in each item.#### Number of problems found: 56

- Complex expr with fractions

Find 1½ of 16 ÷2⅓+(2¼ of ⅑). Use the correct order of operations. The order is PEMDAS: Parentheses, Exponents, Multiplication, Division (from left to right), addition, and Subtraction (from left to right). - 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 complex eq

If z=x+yi and 3x+(3x-y)i=4-6i then z=

- Complex equation

If c - d = 2 and c = 12 + 7 i, find d. Write the result in the form of a + bi. - Suppose 10

Suppose 4+7i is a solution of 5z2+Az+B=0, where A, B∈R. Find A and B. - Let z 2

Let z = 2 - sqrt(3i). Find z^{6}and express your answer in rectangular form. if z = 2 - 2sqrt(3 i) then r = |z| = sqrt(2 ^ 2 + (- 2sqrt(3)) ^ 2) = sqrt(16) = 4 and theta = tan -2√3/2=-π/3 - Find all 2

Find all the complex solutions (write the answer in the form x+iy) of the system. {|z-12|/|z-8i|=5/3 ; |z-4|=|z-8| - Midpoint between conjugate

Find the midpoint between two roots: 2+3.464i and 2 - 3.464i

- Subtract polar forms

Solve the following 5.2∠58° - 1.6∠-40° and give answer in polar form - Conjugate coordinates

If the rectangular conjugate of the polar vector 12 angle 35 degrees is equal to x+yi, find the sum of x and y. - EE school boarding

Three vectors, A, B, and C, are related as follows: A/C = 2 at 120 deg, A + B = -5 + j15, C = conjugate of B. Find C. - 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 the market to sell eggs, and they had 100. When they sold all the eggs, they made the same money. The first grandmother said to the second, "If I sold my eggs for your price, I would earn 15 crowns. " The other grandmother replied - 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.

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