2. Consider z1 = 2 − i and z2 = 2 + 2i. (a) Write the comlex numbers z1z2 and z1/z2 in the form x + iy.

Consider the equation (6 + 7 i) z³ = 5(3 - 5 i). (i) Rearrange the equation into the form z³ = zo where zo is in the simplified complex form a + i b. (ii) Rewrite zo in polar form, using cis or exponential notation.

1.2. Perform arithmetic operations using the polar and exponential form of complex numbers. Complex numbers can be represented in both polar and exponential forms, which offer unique advantages for various mathematical operations. Let Z1 and Z2 be two complex numbers represented in polar form as Z₁ = √₁eiе₁ and Z₂ = 12e102. Perform the following arithmetic operations: i) ii) iii) iv) Calculate Z₁ + Z2 in polar form and express the result as Z3 = re¹03 and in exponential form. Calculate Z1 - Z2 in polar form and express the result as Z4 = √₁e¹04 and in exponential form. Calculate Z1. Z2 in polar form and express the result as Z5 = r5e" form. Calculate Z1 Z2 in polar form and express the result as Z6 = re form. 105 and in exponential 106 and in exponential v) Reflect on the advantages of using polar and exponential forms for complex number operations and how they simplify certain calculations.

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