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Complex Numbers and Quadratic Equations

Short Answer Type

41.

Find the number of non-zero integral solutions of the equation.

$space space space space space space space space space space space space open vertical bar 1 minus straight i close vertical bar to the power of straight x space equals 2 to the power of straight x space end exponent$

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42.

If $space space straight alpha space and space straight beta$ are two different complex number with $space space space space space space space open vertical bar straight beta close vertical bar space equals space 1 space then space find space open vertical bar fraction numerator straight beta minus straight alpha over denominator 1 minus top enclose straight alpha straight beta end fraction close vertical bar$

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43.
If (a + ib) (c+id)(e+if)(g+ih) = A+iB, then show that : (a²+ b²) (c²+ d²) (e²+ f²) (g²h²) = A²+ B²

Here, (a + ib) (c+id)(e+if)(g+ih) = A+iB

Taking modulus, on both sides, we get

Squaring both sides, we get

(a²+ b²) (c²+ d²) (e²+ f²) (g²h²) = A²+ B²

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44.

Convert the following in the polar form.

$space space space space space space space space left parenthesis straight i right parenthesis space space space space space fraction numerator 1 plus 7 straight i over denominator left parenthesis 2 minus straight i right parenthesis squared end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space left parenthesis ii right parenthesis space space space space space fraction numerator 1 plus 2 straight i over denominator 1 minus 3 straight i end fraction$

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45.

Find the values of x and y, if.

3x + (-2x + y) i = 6-2i

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46.

Find the values of x and y, if.

(2x + y - 5) + (3x - 2y - 4) i = 0

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47.

Find the values of x and y, if.

$space space space space space space space space space space fraction numerator open parentheses 1 space plus space straight i close parentheses space straight x space minus space 2 straight i over denominator 3 space plus space straight i end fraction plus fraction numerator left parenthesis 2 minus 3 straight i right parenthesis space straight y space plus space straight i over denominator 3 space minus space straight i end fraction space equals space straight i$

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48.

Write the conjugates of the following complex numbers :

$space space space space space space space space space space space minus space 5 space plus 1 half straight i$

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49.

Write the conjugates of the following complex numbers :

$space space space space space space space space space 7 over 5$

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50.

Write the conjugates of the following complex numbers :

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Previous Year Papers

Test Series

Test Yourself

Short Answer Type

43. If (a + ib) (c+id)(e+if)(g+ih) = A+iB, then show that : (a2 + b2) (c2 + d2 ) (e2 + f2 ) (g2 h2 ) = A2 + B2

43.
If (a + ib) (c+id)(e+if)(g+ih) = A+iB, then show that : (a²+ b²) (c²+ d²) (e²+ f²) (g²h²) = A²+ B²