Complex numbers - high school - practice problems
Number of problems found: 52
- 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 z6 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. - 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? - 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. - Imaginary numbers
Find two imaginary numbers whose sum is a real number. How are the two imaginary numbers related? What is their sum? - Real and imaginary parts
Let z1=x1+y1i and z2=x2+y2i Find: a = Im (z1z2) b = Re (z1/z2) - ReIm notation
Let z = 6 + 5i and w = 3 - i. Compute the following and express your answer in a + bi form. w + 3z - Evaluate 18
Evaluate the expression (-4-7i)-(-6-9i) and write the result in the form a+bi (Real + i* Imaginary).
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