# 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)=36x^{2}-12x+5 h(x)=x^{2}-4x+20 f(x)=4x^{2<} - 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: z_{1}=(-8+i) and z_{2}=(-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 - Bearing

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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