# Complex numbers - practice problems

#### Number of problems found: 43

- 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. - 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 inc - 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. - 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? - 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 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 - 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. - Imaginary numbers

Find two imaginary numbers whose sum is a real number. How are the two imaginary numbers related? What is their sum? - De Moivre's formula

There are two distinct complex numbers z, such that z³ is equal to 1 and z is not equal to 1. Calculate the sum of these two numbers. - 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 - Let z1=x1+y1i

Let z1=x1+y1i and z2=x2+y2i Find: a = Im (z1z2) b = Re (z1/z2) - Evaluate 18

Evaluate the expression (-4-7i)-(-6-9i) and write the result in the form a+bi (Real + i* Imaginary). - 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. - Determine 4083

Determine the sum of complex numbers: 2i² + 2i^{4} - Calculate 3884

Calculate the ratio of the two fifth roots of the number 32. - Is complex

Are these numbers 2i, 4i, 2i + 1, 8i, 2i + 3, 4 + 7i, 8i, 8i + 4, 5i, 6i, 3i complex? - Complex number coordinates

Which coordinates show the location of -2+3i

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