4. Evaluate and convert into polar form. √√2+ = = = 3 2i -√8-2²/1 3

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.

Larsen Califor x e Complex Numbers and DeMoivre x f2.app.edmentum.com/assessments-delivery/ua/mt/launch/4898827 Next O Select the correct answer. Complex Numbers and DeMoivre's Th Convert 1 + i to polar form. O In what bo A. √/2cis ³ B. √2cis/ C. √2cis D. D. √2cis0

given z1=8-8i, z2=-5+5i find z1z2 and write the product in polar form

Write z1 and z2 in polar form. Z1 = -V2i, z2 = -4 – 4/3i Z1 = 22 1 and Z1 Z1 (Express your answers in polar form.) Find the product z1z2 and the quotients Z2 Z1 22 1 Z1