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

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

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To express \((5 - 3i)^3\) in the form \(a + ib\), we will follow these steps: ### Step 1: Expand \((5 - 3i)^3\) We can use the binomial theorem or direct multiplication. Here, we will use direct multiplication. \[ (5 - 3i)^3 = (5 - 3i)(5 - 3i)(5 - 3i) \] ...
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NCERT ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If 4x + i(3x-y) = 3 + i (-6), where x and y are real numbers, then fin...

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. If (a" "+" "i b)" "(c" "+" "i d)" "(e" "+" "if)" "(g" "+" "i h)" "=" "...

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  17. Convert of the complex number in the polar form: 1-i

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  18. Let z1=2-i ,z2=-2+i. Find (i) Re ((z1z2)/( bar z1)) (ii) Im(1/(z1 b...

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  19. Find the modulus and argument of the complex number (1+2i)/(1-3i).

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  20. If z1=2-i ,z2=1+i ,find |(z1+z2+1)/(z1-z2+i)|

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