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Complex Numbers Worksheets

Complex numbers is vital in high school math. Perform operations like addition, subtraction and multiplication on complex numbers, write the complex numbers in standard form, identify the real and imaginary parts, find the conjugate, graph complex numbers, rationalize the denominator, find the absolute value, modulus and argument in this collection of complex number worksheets.

Write in standard form

Access these worksheets to introduce complex numbers to high-school students. Rewrite the given complex number in the standard form (a + bi), where a is the real part, and b is the imaginary part.

Identifying real and imaginary part

The complex numbers are listed in a tabular format. Students are required to identify the real part and the imaginary part. The worksheet also provides practice in forming complex numbers with the given real part and the imaginary part.

Find the conjugate

Download our instantly printable pdf's to find the conjugate of the given complex number. Change the sign of the imaginary part of the complex number to find the complex conjugate.

Evaluating powers of i

Explore this compilation of innovative resources to learn how to simplify powers of i. To solve the problems, apply the power-of-power rule to rewrite each expression to the power of i 2, i 3 or i 4.

Graphing complex numbers

The x-axis and y-axis of the complex coordinate plane represent the real part and imaginary part respectively. Write each complex number a + bi as an ordered pair (a, b). Plot the point on the graph that represents the complex number.

Addition and subtraction

Introduce these worksheets in the classroom to learn the basics of addition and subtraction of complex numbers. Add or subtract the corresponding real parts and the imaginary parts of the complex numbers to find the sum or difference.

Multiplication of complex numbers

Use the FOIL method or the formula (a+bi)(c+di) = (ac−bd) + (ad+bc)i to find the product of the complex numbers. Cross-check your answers with the answer key provided.

Rationalize the denominator

Rationalize the denominator by multiplying the numerator and denominator by the complex conjugate of the denominator. Simplify the expression and write it in the standard form a + bi.

Simplify

This batch of worksheets is an excellent resource for students to practice addition, subtraction, multiplication and division of complex numbers.

Finding absolute value or modulus

The absolute value of a complex number represents the distance between the complex number and the origin in the complex coordinate plane. To find the absolute value or modulus of the complex number, find the square root of sum of the squares of the real part and the imaginary part.

Finding absolute value and argument

Engage students on finding the absolute value and argument of the complex number. Apply the formula θ = tan−1 (y/x) to find the argument of the complex number, which is the angle it makes with the real axis.