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Find the multiplicative inverse of 2-3i....

Find the multiplicative inverse of `2-3i`.

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To find the multiplicative inverse of the complex number \(2 - 3i\), we follow these steps: ### Step 1: Understand the multiplicative inverse The multiplicative inverse of a complex number \(z\) is given by \(z^{-1} = \frac{1}{z}\). Here, \(z = 2 - 3i\). ### Step 2: Write the expression for the inverse We need to calculate: \[ ...
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NCERT ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Convert of the complex number in the polar form: sqrt(3)+i

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  2. Express (-sqrt(3)+sqrt(-2))(2sqrt(3)-i)in the form of a + i b

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  3. Find the multiplicative inverse of 2-3i.

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  4. Express the following in the form a + i b(i) (5+sqrt(2i))/(1-sqrt(2i))...

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  5. Represent the complex number z = 1 +isqrt(3)in the polar form.

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  6. If 4x + i(3x-y) = 3 + i (-6), where x and y are real numbers, then fin...

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  7. Express the following in the form of a + b i:(i) (-5i)(1/8i) (ii) (-i...

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  8. Express (5-3i)^3in the form a + i b.

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  9. Express of the complex number in the form a + i b. (1/3+3i)^3

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  10. Express of the complex number in the form a + i b. (1-i)^4

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  11. Express of the complex number in the form a + i b. i^-39

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  12. Express of the complex number in the form a + i b. i + i

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  13. Express of the complex number in the form a + i b. (5i)(-3/5i)

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  14. Express of the complex number in the form a+ib. [(1/3+i7/3)+(4+i1/3)]...

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  15. Express of the complex number in the form a + i b. (1/5+i2/5)-(4+i5/2)

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  16. Express of the complex number in the form a + i b. (1 - i) - (- 1 + i...

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  17. Express of the complex number in the form a + i b. 3(7 + i7) + i(7 + ...

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  18. If x - i y =sqrt((a-i b)/(c-i d)) prove that x^2+y^2=(a^2+b^2)/(c^2+d^...

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  19. Find the number of non-zero integral solutions of the equation |1-i|^...

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  20. Solve the equation: x^2 + x/sqrt2 + 1 =0

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