Question

Express the following expressions as a + ib

$(5 - 3i) {}^{3}$

Answer 1

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$\bold{\underline{Question-}}$

Express the following expressions as a + ib

$(5 - 3i) {}^{3}$



$\bold{\underline{Answer-}}$


$(5 - 3i) {}^{3} = {5}^{3} - 3( {5}^{2} ) {(3i)}^{} + 3(5) {(3i)}^{2} - {(3i)}^{3} \\ \\ =125 - 225i + 135i {}^{2} - 27 {i}^{3} \\ \\ = 125 - 225i - 135 - {27i}^{2} .i \\ \\ = - 10 - 225i + 27i \\ \\ = - 10 - 198i$

Answer 2

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Here is your answer

$(5 - 3i) {}^{3} \\ = {5}^{3} - (3i) {}^{3} - 3 \times 5 {}^{2} \times 3i + 3 \times 5 \times (3i) {}^{2} \\ = 125 - 27i {}^{3} - 225i + 135i {}^{2} \\ = 125 - 27 \times {i}^{2} \times i - 225i - 135 \\ = 125 + 27i - 225i - 135 \\ = - 10 - 198i$

Therefore
a= -10
b = -198

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