Exploring Midpoint and Distance in the Complex Plane

The video tutorial explains how to plot two complex numbers, z and w, on the complex plane. It then demonstrates how to calculate the distance between these numbers using the Pythagorean theorem. Finally, it shows how to find the complex number that is exactly halfway between z and w, which involves calculating the midpoint of their real and imaginary parts.

What are the complex numbers z and w introduced in the video?

• z = -2 + 3i, w = 5 + i

• z = 2 + 3i, w = -5 - i

• z = 2 - 3i, w = 5 - i

• z = 3 + 2i, w = -5 + i

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CCSS.HSN.CN.A.1

What is the real part of the complex number z?

• 3

• 2

• -1

• -5

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CCSS.HSN.CN.A.1

Where is the complex number w located on the complex plane?

• (2, 3)

• (-5, -1)

• (5, 1)

• (-2, -3)

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CCSS.HSN.CN.B.4

What is the distance between the complex numbers z and w?

• Square root of 65

• Square root of 81

• Square root of 16

• Square root of 49

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CCSS.HSN.CN.B.6

Which theorem is used to calculate the distance between z and w?

• Pythagorean theorem

• Binomial theorem

• Euclidean algorithm

• Fundamental theorem of algebra

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CCSS.HSN.CN.B.4

What is the change in the real axis when moving from w to z?

• 4

• 7

• 2

• 5

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CCSS.HSN.CN.B.4

What is the imaginary part of the midpoint between z and w?

• 1

• 2

• 3

• 4

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CCSS.HSN.CN.B.6

How do you find the real part of the midpoint between two complex numbers?

• By subtracting the imaginary parts and dividing by 2

• By adding the real parts and dividing by 2

• By subtracting the real parts and dividing by 2

• By adding the imaginary parts and dividing by 2

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CCSS.HSN.CN.B.6

What is the real part of the midpoint between z and w?

• -3/2

• 3/2

• 1/2

• -1/2

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CCSS.HSN.CN.B.6

Where is the midpoint between z and w located on the complex plane?

• (-1.5, 1)

• (1.5, -1)

• (1.5, 1)

• (-1.5, -1)

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CCSS.HSN.CN.B.6