Free Complex Number Lesson Plan for 10th Grade Students

Topic: complex number

Objectives & Outcomes

• To understand the concept of complex number and its applications
• To be able to solve problems involving complex number

Materials

• Complex numbers represented in the form a + bi (where a and b are real numbers and i is the imaginary unit)
• Computer with a graphing calculator
• Worksheets for practice problems

Warm-up

• Ask students to give their own definition of a complex number.
• Ask students to give examples of complex numbers using a + bi representation.
• Ask students to solve problems involving complex numbers using a + bi representation.

Direct Instruction

• Introduce the concept of a complex number as a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, where i2 = -1.
• Explain the properties of a complex number, including the following:
• *the magnitude of a complex number is given by the formula a + bi, which is the distance of the point (a,b) from the origin
• *the direction of a complex number is given by the direction of the vector (a,b)
• *the conjugate of a complex number is given by the formula a - bi, where the conjugate of a complex number is its mirror image over the origin
• *the modulus of a complex number is given by the formula a + bi, which is the distance of the point (a,b) from the origin
• *the argument of a complex number is given by the formula arg(a + bi), where arg(a + bi) = the angle in radians between the positive x-axis and the vector (a,b)
• *the real part of a complex number is given by the formula re(a + bi), where re(a + bi) is the real part of a + bi
• *the imaginary part of a complex number is given by the formula im(a + bi), where im(a + bi) is the imaginary part of a + bi
• *the conjugate conjugate of a complex number is given by the formula a + bi*a - bi, where the conjugate conjugate of a complex number is its mirror image over the origin
• *the conjugate of the conjugate of a complex number is given by the formula a + bi*a - bi*a + bi, where the conjugate of the conjugate of a complex number is its mirror image over the origin
• *the complex conjugate of a complex number is given by the formula a + bi*a - bi, where the complex conjugate of a complex number is its mirror image over the origin
• *the sum of two complex numbers is given by the formula a + bi + a' + bi', where a + bi and a' + bi' are the real parts and a' + bi' is the imaginary part of the two complex numbers
• *the difference of two complex numbers is given by the formula a + bi - a' + bi', where a + bi and a' + bi' are the real parts and a' + bi' is the imaginary part of the two complex numbers
• *the product of two complex numbers is given by the formula a*a' + bi*bi' + a'*a'', where a and a' are the real parts and bi and bi

Guided Practice

• Give the complex number in the form a + bi
• Give the magnitude, direction, and argument of the complex number
• Give the real part, imaginary part, and complex conjugate of the complex number
• Give the modulus, argument, and complex conjugate of the complex number
• Give the sum, difference, and product of the complex numbers a + bi and a' + bi'
• Give the complex conjugate of the complex number a + bi
• Give the complex conjugate of the complex conjugate of the complex number a + bi
• Go through the steps to simplify a complex fraction, such as a + bi/a' + bi'
• Give examples of complex numbers, including the following:
• *the number 2 + 3i
• *the number -3 + 2i
• *the number 5 - 6i
• *the number -7 + 8i
• *the number -10 + 11i
• *the number -13 + 14i
• *the number -16 + 17i
• *the number -19 + 20i
• *the number -23 + 24i
• *the number -26 + 27i
• *the number -29 + 30i
• *the number -32 + 33i
• *the number -35 + 36i
• *the number -38 + 39i
• *the number -41 + 42i
• *the number -44 + 45i
• *the number -47 + 48i
• *the number -50 + 51i
• *the number -53 + 54i
• *the number -56 + 57i
• *the number -59 + 60i
• *the number -62 + 63i
• *the number -65 + 66i
• *the number -68 + 69i
• *the number -71 + 72i
• *the number -74 + 75i
• *the number -77 + 78i
• *the number -80 + 81i
• *the number -83 + 84i
• *the number -86 + 87i
• *the number -89 + 90i
• Give the summary of the properties of complex numbers
• Ask questions to check for understanding

Guided Practice

• Give complex numbers in the form a + bi
• Calculate the real part, imaginary part, and complex conjugate of the complex numbers
• Calculate the modulus, argument, and complex conjugate of the complex numbers
• Calculate the sum, difference, and product of the complex numbers
• Calculate the complex conjugate of the complex numbers
• Calculate the complex conjugate of the complex conjugate of the complex numbers

Independent Practice

• Give complex numbers in the form a + bi
• Calculate the real part, imaginary part, and complex conjugate of the complex numbers
• Calculate the modulus, argument, and complex conjugate of the complex numbers
• Calculate the sum, difference, and product of the complex numbers
• Calculate the complex conjugate of the complex numbers
• Calculate the complex conjugate of the complex conjugate of the complex numbers
• Go through the steps to simplify a complex fraction, such as a + bi/a' + bi'
• Give examples of complex numbers, including the following:
• *the number 2 + 3i
• *the number -3 + 2i
• *the number 5 - 6i
• *the number -7 + 8i
• *the number -10 + 11i
• *the number -13 + 14i
• *the number -16 + 17i
• *the number -19 + 20i
• *the number -23 + 24i
• *the number -26 + 27i
• *the number -29 + 30i
• *the number -32 + 33i
• *the number -35 + 36i
• *the number -38 + 39i
• *the number -41 + 42i
• *the number -44 + 45i
• *the number -47 + 48i
• *the number -50 + 51i
• *the number -53 + 54i
• *the number -56 + 57i
• *the number -59 + 60i
• *the number -62 + 63i
• *the number -65 + 66i
• *the number -68 + 69i
• *the number -71 + 72i
• *the number -74 + 75i
• *the number -77 + 78i
• *the number -80 + 81i
• *the number -83 + 84i
• *the number -86 + 87i
• *the num

er -89 + 88i

• *the numer -91 + 92i
• *the numer -93 + 94i
• *the numer -95 + 96i
• *the numer -97 + 98i
• *the numer -99 + 100i
• *the numer -102 + 103i
• *the numer -104 + 105i
• *the numer -106 + 107i
• *the numer -108 + 109i
• *the numer -110 + 111i
• *the numer -112 + 113i
• *the numer -114 + 115i
• *the numer -116 + 117i
• *the numer -118 + 119i
• *the numer -120 + 121i
• *the numer -122 + 123i
• *the numer -124 + 125i
• *the numer -126 + 127i
• *the numer -128 + 129i
• *the numer -130 + 131i
• *the numer -132 + 133i
• *the numer -134 + 135i
• *the numer -136 + 137i
• *the numer -138 + 139i
• *the numer -140 + 141i
• *the numer -142 + 143i
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181 + 182i

• *the numer -183 + 184i
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• *the numer -272 +