4) Simplify the following and express in the form a + ib.
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5(4 - √15)/17 + 3i (4 - √15)l17
Step-by-step explanation:
( √5 + √3i) ÷ ( √5 - √3i) = ( √5 + √3i)( √5 + √3i) ÷ ( √5 - √3i)( √5 + √3i)
= (8 - 2√15) ÷ (5 - 3i) = (8 - 2√15)(5 + 3i) ÷ (5 - 3i)(5 + 3i) = (8 - 2√15)(5 + 3i) ÷34
= (4 - √15)(5 + 3i) ÷17 = 5(4 - √15)/17 + 3i (4 - √15)l17
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a= 1/4
ib= √15i/4. Ans.
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