Math Problem Solver

For the complex numbers w_1 = 2 + 5i and w_2 = -1 + 2i,

Represent w_1 and w_2 on the same Argand diagram. [2]

For each of the following involving w_1 and w_2 as described above, a pair of expression is given. Demonstrate algebraically what single complex number each expression evaluates to. Then, for each pair, add them to the Argand diagram as in parts above. Use a new diagram for each pair. For each pair comment on the commutative nature of complex numbers under the operation.

w_1 + w_2; w_2 + w_1 [3]

w_1 × w_2; w_2 × w_1 [3]

w_1/w_2 ; w_2/w_1 [4]

For an arbitrary complex number, 𝑧, represent the following on a new Argand diagram. Also, give a geometric interpretation.

|z - w_2 | < 3 [6]

Overall presentation and formatting of assignment