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: 59
- Real and imaginary parts
Let z1=x1+y1i and z2=x2+y2i Find: a = Im (z1z2) b = Re (z1/z2) - 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) - ReIm notation
Let z = 6 + 5i and w = 3 - i. Compute the following and express your answer in a + bi form. w + 3z - Evaluate complex expr Evaluate the expression (-4-7i)-(-6-9i) and write the result in the form a+bi (Real + i* Imaginary).
- Imaginary numbers
Find two imaginary numbers whose sum is a real number. How are the two imaginary numbers related? What is their sum? - 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. - Log
Calculate the value of expression log |-10 -2i +7i²| . - 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
- Complex sum
Determine the sum of complex numbers: 2i² + 2i4 - Is complex Are these numbers 2i, 4i, 2i + 1, 8i, 2i + 3, 4 + 7i, 8i, 8i + 4, 5i, 6i, 3i complex?
- Difference - two complex
Determine the difference between two complex numbers: 3i²-3i4 - Complex number coordinates
Which coordinates show the location of -2+3i - 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 - Im>0?
Is -5i a positive number? - Reciprocal Calculate the reciprocal of z=0.8-1.8i:
- 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 - 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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