Solve - 3-4i4-5i4-3i6-7i

(3+4i)(4+5i) (4+3i)(6+7i) = 12+15i+16i+20 i ^ 2 24+28i+18i+21 i ^ 2 = 12+31i 20 24+46i 21 (∵ i ^ 2 = 1) = 31i 8 46i 3 × 46i+3 46i+ ...

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Byju's Answer

Standard XII

Mathematics

Complex Numbers

Solve : 3+4...

Question

Solve : $\frac{(3 + 4 i) (4 + 5 i)}{(4 + 3 i) (6 + 7 i)}$

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Solution

$\frac{(3 + 4 i) (4 + 5 i)}{(4 + 3 i) (6 + 7 i)} = \frac{12 + 15 i + 16 i + 20 i^{2}}{24 + 28 i + 18 i + 21 i^{2}} = \frac{12 + 31 i - 20}{24 + 46 i - 21} (∵ i^{2} = - 1) = \frac{31 i - 8}{46 i - 3} \times \frac{46 i + 3}{46 i + 3} = \frac{11 i + 58}{85}$

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Similar questions

Q. If

A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 - 3 i & 3 + 4 i 2 + 3 i & 0 & 4 - 5 i 3 - 4 i & 4 + 5 i & 2 \end{matrix} ⎤ ⎥ ⎦

then A is

Q. Prove that the value of the determinant

⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} - 7 & 5 + 3 i & \frac{2}{3} - 4 i 5 - 3 i & 8 & 4 + 5 i \frac{2}{3} + 4 i & 4 - 5 i & 9 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

is real.

Imaginary part of third element of the second row for the Conjugate of $⎡ ⎢ ⎣ \begin{matrix} 3 + 4 i & 4 & 2 + 5 i 1 + 2 i & 2 + 3 i & 3 + 5 i 2 + 7 i & 9 & 5 \end{matrix} ⎤ ⎥ ⎦$ is

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Q. Solve

(3 - 7 i) + (- 2 + 4 i)

Q. Solve for

z : z^{2} - (3 - 2 i) z = (5 i - 5)

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Solve : (3+4i)(4+5i)(4+3i)(6+7i)

(3+4i)(4+5i)(4+3i)(6+7i)=12+15i+16i+20i224+28i+18i+21i2=12+31i−2024+46i−21(∵i2=−1)=31i−846i−3×46i+346i+3=11i+5885

Solve : $\frac{(3 + 4 i) (4 + 5 i)}{(4 + 3 i) (6 + 7 i)}$

$\frac{(3 + 4 i) (4 + 5 i)}{(4 + 3 i) (6 + 7 i)} = \frac{12 + 15 i + 16 i + 20 i^{2}}{24 + 28 i + 18 i + 21 i^{2}} = \frac{12 + 31 i - 20}{24 + 46 i - 21} (∵ i^{2} = - 1) = \frac{31 i - 8}{46 i - 3} \times \frac{46 i + 3}{46 i + 3} = \frac{11 i + 58}{85}$