If 3-5 i 3 can be expressed in the form a - ib-then the ordered pair a - b isA- -198-10B- -198-10C- 198-10D- 198-10

We know that (z_1 z_2)^3=z_1^3 z_2^3 3z_1z_2(z_1 z_2) ∴ (3 5i)^3 =3^3 (5i)^3 3× 3 × 5i(3 5i) =27 125i^3 135i+225i^2 =27+125i 135i 225 ∵ [ i^3= i, i^2= 1] = 19 ...

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Standard XII

Mathematics

Distance Formula Using Complex Numbers

If 3-5 i 3 ca...

Question

If $(3 - 5 i)^{3}$ can be expressed in the form $a + i b$ ,then the ordered pair $(a, b)$ is

(- 198, 10)

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(- 198, - 10)

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(198, - 10)

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(198, 10)

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Solution

The correct option is B $(- 198, - 10)$
We know that $(z_{1} - z_{2})^{3} = z_{1}^{3} - z_{2}^{3} - 3 z_{1} z_{2} (z_{1} - z_{2}) .$
$∴ (3 - 5 i)^{3} = 3^{3} - (5 i)^{3} - 3 \times 3 \times 5 i (3 - 5 i)$
$= 27 - 125 i^{3} - 135 i + 225 i^{2}$
$= 27 + 125 i - 135 i - 225 ∵ [i^{3} = - i, i^{2} = - 1]$
$= - 198 - 10 i$ .

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Distance Formula Using Complex Numbers

Standard XII Mathematics

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If (3−5i)3 can be expressed in the form a+ib ,then the ordered pair (a,b) is

The correct option is B (−198,−10)We know that (z1−z2)3=z31−z32−3z1z2(z1−z2). ∴(3−5i)3=33−(5i)3−3×3×5i(3−5i) =27−125i3−135i+225i2 =27+125i−135i−225 ∵[i3=−i,i2=−1] =−198−10i.

If $(3 - 5 i)^{3}$ can be expressed in the form $a + i b$ ,then the ordered pair $(a, b)$ is