Multiply and Divide Complex Numbers 100%

Review the graphs of complex numbers z and w. What is the product of z and w?

A. -20 + 10i

Let z = 5 - 9i and w = 6 + i. Which expression shows the first step in finding the quotient of z/w?

A. 5-9i/6+i * 6-i/6-i

For the complex numbers z = 30 (cos(2pi/3) + isin(2pi/3)) and w = 6 (cos(pi/8) + isinpi/8) , which geometric transformation of z on the complex plane describes the quotient z/w?

A. Scale z by a factor of 1/6, then rotate clockwise by pi/8 radians.

What is 56(cos(33°) + i sin(33°)) ÷ 7(cos(11°) + i sin(11°))?

C. 8(cos(22°) + i sin(22°))

Which phrase describes the geometric interpretation of dividing a complex number z by i?

C. Rotate z by 90° clockwise about the origin.

Which statement describes how to geometrically divide a complex number, z, by a second complex number, w?

C. Scale z by the reciprocal of the modulus of w, then rotate clockwise by the argument of w.

Let z = 0.3(cos(31°) + i sin(31°)) and w = 20(cos(18°) + i sin(18°)). Which statement describes the geometric construction of the product zw on the complex plane?

C. Stretch z by a factor of 20, then rotate 18° counterclockwise.

Review the graphs of complex numbers z and w. What is z/w?

D. 8+2i

For z = 13 + 13i and w = StartRoot 6 EndRoot + i , which geometric transformation describes the product of z and w on the coordinate plane?

D. Scale w by a factor of 13StartRoot 2 EndRoot and rotate 45° counterclockwise.

For z = -3 - 5i, which graph shows z and the product of z · i?

Graph A