Mrs. Rivas International Studies Charter School.Objective: Plot complex numberPlot complex number in the complex plane. absolute valueFind the absolute value of a complex number. Writein polar formWrite complex numbers in polar form. Convertfrom polar to rectangularConvert a complex number from polar to rectangular form. Find productsFind products of complex numbers in polar form. Find powersFind powers of complex numbers in polar form. Find rootsFind roots of complex numbers in polar form.
Mrs. Rivas International Studies Charter School. The Complex Plane
Mrs. Rivas International Studies Charter School. We plot the point (a, b) = (2, 3).
Mrs. Rivas International Studies Charter School. We plot the point (a, b) = (–3, –5).
Mrs. Rivas International Studies Charter School. We plot the point (a, b) = (–4, 0).
Mrs. Rivas International Studies Charter School. We plot the point (a, b) = (0, –1).
Mrs. Rivas International Studies Charter School. The Absolute Value of a Complex Number
Mrs. Rivas International Studies Charter School.
Mrs. Rivas International Studies Charter School.
Mrs. Rivas International Studies Charter School. Polar Form of a Complex Number
Mrs. Rivas International Studies Charter School.
Mrs. Rivas International Studies Charter School.
Mrs. Rivas International Studies Charter School.
Mrs. Rivas International Studies Charter School.
Mrs. Rivas International Studies Charter School. Products and Quotients in Polar Form We can multiply and divide complex numbers fairly quickly if the numbers are expressed in polar form.
Mrs. Rivas International Studies Charter School. Find the product of the complex numbers. Leave the answer in polar form.
Mrs. Rivas International Studies Charter School. Find quotients of complex numbers in polar form.
Mrs. Rivas International Studies Charter School. Find the quotient of the following complex numbers. Leave the answer in polar form.
Mrs. Rivas International Studies Charter School. Powers of Complex Numbers in Polar Form DeMoivre’s Theorem The formula for the nth power of a complex number is known as DeMoivre’s Theorem in honor of the French mathematician Abraham DeMoivre (1667–1754).
Mrs. Rivas International Studies Charter School.
Mrs. Rivas International Studies Charter School.
Mrs. Rivas International Studies Charter School. v v
Mrs. Rivas International Studies Charter School. Roots of Complex Numbers in Polar Form
Mrs. Rivas International Studies Charter School. Roots of Complex Numbers in Polar Form
Mrs. Rivas International Studies Charter School. There are exactly four fourth roots of the given complex number. The four fourth roots are found by substituting 0, 1, 2, and 3 for k in the expression
Mrs. Rivas International Studies Charter School.
Mrs. Rivas International Studies Charter School.
Mrs. Rivas International Studies Charter School.
Mrs. Rivas International Studies Charter School. The four complex fourth roots are:
Mrs. Rivas International Studies Charter School. Find all the cube roots of 8. Write roots in rectangular form.
Mrs. Rivas International Studies Charter School. Find all the cube roots of 8. Write roots in rectangular form.
Mrs. Rivas International Studies Charter School. Find all the cube roots of 8. Write roots in rectangular form.
Mrs. Rivas International Studies Charter School. Find all the cube roots of 8. Write roots in rectangular form.
Mrs. Rivas International Studies Charter School. Find all the cube roots of 8. Write roots in rectangular form.
Mrs. Rivas Pg # Even 30, 32, 42, 44, 46, 48, 52, 54, 58, 62, 66, 70, 72, 76