Homework SourseWrite the expression in standard form 1 3i5 3iSolutionGive
Write the expression in standard form. 1 + 3i/5 + 3i![Write the expression in standard form. 1 + 3i/5 + 3iSolutionGiven that (1 + 3i) / (5+3i) Multiply both numerator and denominator by 5-3i = [ (1 + 3i) / (5+3i)]](/WebImages/37/write-the-expression-in-standard-form-1-3i5-3isolutiongive-1111001-1761589079-0.webp "Write the expression in standard form. 1 + 3i/5 + 3iSolutionGiven that (1 + 3i) / (5+3i) Multiply both numerator and denominator by 5-3i = [ (1 + 3i) / (5+3i)]")
Solution
Given that (1 + 3i) / (5+3i)
Multiply both numerator and denominator by 5-3i
= [ (1 + 3i) / (5+3i)] x [(5- 3i) / (5-3i)]
= [ (1 + 3i) (5- 3i) / (5+3i) (5-3i)]
= ( 5 -3i + 15i + 9 ) / ( 25+9) [ (a+bi) (a-bi) = a2 +b2 ] and [ i2 =-1 ]
= (14 + 12i )/ 34
= (7 + 6i)/ 17
= (7/17) + (6/17) i
Therefore,
(1 + 3i) / (5+3i) = (7/17) + (6/17) i
