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Back to Represent operations geometrically — Problem 5 · Task Set 11

Exercises: Represent Operations Geometrically on the Complex Plane

Show your work. Use exact values where possible. For polar form, express angles in degrees.

Grade 9·22 problems·~40 min·Common Core Math - HS Number and Quantity·standard·hsn-cn-b-5
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Fluency Practice

1.

The complex number z=1+iz = 1 + i has modulus 2\sqrt{2} and argument $45°$.

Using the multiplication rule ∣z⋅w∣=∣z∣⋅∣w∣|z \cdot w| = |z| \cdot |w| and arg⁡(z⋅w)=arg⁡(z)+arg⁡(w)\arg(z \cdot w) = \arg(z) + \arg(w), compute (1+i)2(1 + i)^2.

What is the modulus of (1+i)2(1 + i)^2? Enter the exact value.