= numerator and denominator] ………[Expand = Note = i2 ……..[Simplify. –1] = ………..[Simplify] = = +i + = i Example 3: If = 3 determine the value of in the form where and b are real numbers. a + bi, a – –5i, Solution: Step 1: Determine the of 1: – 1 = 1 – –3 –5i – 1 = (4 + 5i) – – Step 2: Determine the value of + 1: = 3 5i + 1 + 1 – – + 1 = (2 + 5i) – Step 3: Now proceed to determine the value of: = = by conjugate] ….[Multiply = ….[Expand] = = …..[i2 –1] = = = i – Activity 6 Express each of the following fractions in the form where and are real a + bi, a b numbers. a) b) c) d)
= ………[Expand numerator and denominator] = ……..[Simplify. Note i2 = –1] = ………..[Simplify] = = +i = + i Example 3: If = – 3 –5i, determine the value of in the form a + bi, where a and b are real numbers. Solution: Step 1: Determine the of – 1: – 1 = –3 –5i – 1 – 1 = – (4 + 5i) Step 2: Determine the value of + 1: + 1 = – 3 – 5i + 1 + 1 = – (2 + 5i) Step 3: Now proceed to determine the value of: = = ….[Multiply by conjugate] = ….[Expand] = …..[i2 = –1] = = = – i Activity 6 Express each of the following fractions in the form a + bi, where a and b are real numbers. a) b) c) d)
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