Multiplying Complex Number In Exercises 3146 perform the ope

Multiplying Complex Number In Exercises 31-46 perform the operation and write the result in standard form. 31. 6. 2 32. -5. -10 33. (-10)^2 34. (-75)^2 35. 4(3 + 5i) 36. -6(5 - 3i) 37. (1 + i)(3 - 2i) 38. (6 - 2i)(2 - 3i)

Solution

31) (6i) (2i) = (6.2)i² = 12(-1) {Using i²=-1}

=> -12

32) (5i).(10i) = (5.10)(i²) = 50(-1) = -50

33) (10i)² = (10i)(10i) = 100i² = -100

34) (75i)² = (75i)(75i) = 5625i² = -5625

35) 4(3+5i) = 4.3+4.5i = 12+20i

36) -6(5-3i) = -6.5-6.-3i = -30+18i

37) (1+i).(3-2i) = 1.3+1(-2i)+i.3+i(-2i) = 3-2i+3i-2i² = 3+(3-2)i-2(-1) = 3+1.i+2 = (3+2)+i = 5+i

38) (6-2i)(2-3i) = 6.2+6.(-3i)-2i.2-2i(-3i)= 12-18i-4i+6i² = 12-(18+4)i+6(-1) = 12-22i-6 = (12-6)-22i = 6-22i