Answers NC-Math 4 CRMultiply and Divide Complex Numbers

Multiply and Divide Complex Numbers Answers

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

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

Scale z by the modulus of w, then rotate counterclockwise by the argument of w.

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

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

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Review the four points on the complex plane.

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

Scale z by a factor of 13 and rotate 30° counterclockwise.

Scale z by a factor of 13 and rotate 45° counterclockwise.

Scale w by a factor of 13 and rotate 30° counterclockwise.

Scale w by a factor of 13 and rotate 45° counterclockwise.

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

On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point z is (negative 3, negative 5) and point z times I is (5, negative 3).

On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point z is (negative 3, negative 5) and point z times I is (3, negative 5).

On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point z is (negative 3, negative 5) and point z times I is (negative 5, 3).

On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point z is (negative 3, negative 5) and point z times I is (negative 3, 5).

Review the graphs of complex numbers z and w.

–20 + 10i

–15 + 5i

8 – 4i

20 – 10i

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

8(cos(3°) + i sin(3°))

49(cos(3°) + i sin(3°))

8(cos(22°) + i sin(22°))

49(cos(22°) + i sin(22°))

For the complex numbers z = and , which geometric transformation of z on the complex plane describes the quotient ?

Scale z by a factor of , then rotate clockwise by radians.

Scale z by a factor of 6, then rotate clockwise by radians.

Scale z by a factor of , then rotate counterclockwise by radians.

Scale z by a factor of 6, then rotate counterclockwise by radians.

What is the product of 16(cos(47°) + i sin(47°)) and 4(cos(12°) + i sin(12°))?

20(cos(35°) + i sin(35°))

20(cos(59°) + i sin(59°))

64(cos(35°) + i sin(35°))

64(cos(59°) + i sin(59°))

Which statement describes how to geometrically determine the product of z = 25 – i and w = + 3i on the complex plane?

Stretch z by a factor of and rotate 30° counterclockwise.

Stretch z by a factor of and rotate 60° counterclockwise.

Stretch z by a factor of and rotate 30° counterclockwise.

Stretch z by a factor of and rotate 60° counterclockwise.

For z = –2 + 2i, which graph represents z and –2z?

On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point z is (negative 2, 2) and point negative 2 z is (1, negative 1).

On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point z is (negative 2, 2) and point negative 2 z is (4, negative 4).

On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point z is (negative 2, 2) and point negative 2 z is (negative 1, negative 4).

On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point z is (negative 2, 2) and point negative 2 z is (negative 4, negative 4).

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Multiply and Divide Complex Numbers Answers

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