Complex numbers - practice problems
Number of problems found: 30
- 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.
- 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 inc
- Evaluate 18
Evaluate the expression (-4-7i)-(-6-9i) and write the result in the form a+bi (Real + i* Imaginary).
- Cis notation
Evaluate multiplication of two complex numbers in cis notation: (6 cis 120°)(4 cis 30°) Write result in cis and Re-Im notation.
- 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.
- ReIm notation
Let z = 6 + 5i and w = 3 - i. Compute the following and express your answer in a + bi form. w + 3z
- Conjugate equation
Find the numbers of a and b, if (a - bi) (3 + 5i) is the Conjugate of (-6 - 24i)
- Eq2 equations
For each of the following problems, determine the roots of the equation. Given the roots, sketch the graph and explain how your sketch matches the roots given and the form of the equation: g(x)=36x2-12x+5 h(x)=x2-4x+20 f(x)=4x2<
- Subtracting complex in polar
Given w =√2(cosine (p/4) + i sine (pi/4) ) and z = 2 (cosine (pi/2) + i sine (pi/2) ), what is w - z expressed in polar form?
- Distance two imaginary numbs
Find the distance between two complex number: z1=(-8+i) and z2=(-1+i).
- Modulus and argument
Find the mod z and argument z if z=i
- Linear combination of complex
If z1=5+3i and z2=4-2i, write the following in the form a+bi a) 4z1+6z2 b) z1*z2
- Two grandmothers
Two grandmothers went to sell eggs at the market, and they had a total of 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 grandmot
- Mappings of complex numbers
Find the images of the following points under mappings: z=3-2j w=2zj+j-1
- Let z1=x1+y1i
Let z1=x1+y1i and z2=x2+y2i Find: a = Im (z1z2) b = Re (z1/z2)
- The modulus
Find the modulus of the complex number 2 + 5i
- Turtles 2
A box turtle hibernates in the sand at 11 5/8. A spotted turtle hibernates at 11 16/25 feet. Which turtle is deeper? Write answer as number 1 or 2.
- Complex number coordinates
Which coordinates show the location of -2+3i
A plane flew 50 km on a bearing 63°20' and the flew on a bearing 153°20' for 140km. Find the distance between the starting point and the ending point.
- Linear imaginary equation
Given that 2(z+i)=i(z+i) "this is z star" Find the value of the complex number z.
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