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Assignment 3 Consider the complex number (MARCH-2012) z=(5-sqrt34)/(4+2sqrt3) i) Express complex number in the form of a + ib. ii) Express complex number in the polar form

Assignment 33\newlineConsider the complex number (MARCH−2012-2012)\newlinez=5−344+23 z=\frac{5-\sqrt{3} 4}{4+2 \sqrt{3}} \newlinei) Express complex number in the form of a + ib.\newlineii) Express complex number in the polar form

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Q. Assignment 33\newlineConsider the complex number (MARCH−2012-2012)\newlinez=5−344+23 z=\frac{5-\sqrt{3} 4}{4+2 \sqrt{3}} \newlinei) Express complex number in the form of a + ib.\newlineii) Express complex number in the polar form
  1. Rationalize Denominator: To express the complex number in the form a+ib a + ib , we need to rationalize the denominator.\newlineCalculation: z=5−344+23×4−234−23 z = \frac{5 - \sqrt{34}}{4 + 2\sqrt{3}} \times \frac{4 - 2\sqrt{3}}{4 - 2\sqrt{3}} \newlinez=(5−34)(4−23)(4+23)(4−23) z = \frac{(5 - \sqrt{34})(4 - 2\sqrt{3})}{(4 + 2\sqrt{3})(4 - 2\sqrt{3})}
  2. Simplify Denominator: Simplify the denominator using the difference of squares formula.\newlineCalculation: (4+23)(4−23)=42−(23)2=16−12=4 (4 + 2\sqrt{3})(4 - 2\sqrt{3}) = 4^2 - (2\sqrt{3})^2 = 16 - 12 = 4
  3. Expand Numerator: Expand the numerator using the distributive property.\newlineCalculation: (5−34)(4−23)=20−103−434+2102 (5 - \sqrt{34})(4 - 2\sqrt{3}) = 20 - 10\sqrt{3} - 4\sqrt{34} + 2\sqrt{102}

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