1. For each pair of vectors, represented as complex numbers, sketch z, w, z + w...

 

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1. For each pair of vectors, represented as complex numbers, sketch z, w, z + w and z-w using a single parallelogram. State the modulus of z, w, z+w and z-w. You may print the complex plane grid on the last page of this document and use it for your sketch. Sketch each pair, and resulting paralellogram, on a separate gird. (a) z=-3-2i and w = 4 +6i (b) z = 5i and w=-4+i 2. Suppose z, w C, and w#0. Prove the following: (a) |zw|=|z||w| |z| 3. Using the results from question 1, find the modulus of the following. -1+2i (-1-i)(3-i) w = 1. For each pair of vectors, represented as complex numbers, sketch z, w, z + w and z-w using a single parallelogram. State the modulus of z, w, z+w and z-w. You may print the complex plane grid on the last page of this document and use it for your sketch. Sketch each pair, and resulting paralellogram, on a separate gird. (a) z=-3-2i and w = 4 +6i (b) z = 5i and w=-4+i 2. Suppose z, w C, and w#0. Prove the following: (a) |zw|=|z||w| |z| 3. Using the results from question 1, find the modulus of the following. -1+2i (-1-i)(3-i) w =