Complex numbers - practice problems - page 2 of 3
Instructions: Solve each problem carefully and provide a detailed solution for every item.Number of problems found: 60
- Real and imaginary parts
Let z1=x1+y1i and z2=x2+y2i Find: a = Im (z1z2) b = Re (z1/z2) - Imaginary numbers
Find two imaginary numbers whose sum is a real number. How are the two imaginary numbers related? What is their sum? - Apartments in complex
A developer offers for sale apartments in a newly built residential complex. In his offer there are the following three types of apartments: MINI – 3 windows, has one balcony, has no garage parking space; MEDIUM – 6 windows, has no balcony, has one garage - Evaluate complex expr
Evaluate the expression (-4-7i)-(-6-9i) and write the result in the form a+bi (Real + i* Imaginary). - 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
- Log
Calculate the value of expression log |-10 -2i +7i²| . - 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)=4x²-24x+45 p(x)=9x²-36x+40 g(x) - 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
- Difference - two complex
Determine the difference between two complex numbers: 3i²-3i4 - Complex sum
Determine the sum of complex numbers: 2i² + 2i4 - Complex number coordinates
Which coordinates show the location of -2+3i - Im>0?
Is -5i a positive number? - Reciprocal Calculate the reciprocal of z=0.8-1.8i:
- Complex conjugate
What is the conjugate of the expression 5√6 + 6√5 i? A.) -5√6 + 6√5 i B.) 5√6 - 6√5 i C.) -5√6 - 6√5 i D.) 6√5 - 5√6i - Is complex Are these numbers 2i, 4i, 2i + 1, 8i, 2i + 3, 4 + 7i, 8i, 8i + 4, 5i, 6i, 3i complex?
- Real roots
Determine the real root of the equation: x-3: x-8 = 32 - Conjugate equation
Find the numbers of a and b; if (a - bi) (3 + 5i) is the Conjugate of (-6 - 24i) - Mappings of complex numbers
Find the images of the following points under mappings: z=3-2j w=2zj+j-1 - Quadratic - EQ2 - complex
Solve the quadratic equation: 2y²-8y + 12 = 0
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