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Complex Numbers and Quadratic Equations

Short Answer Type

11.

Find the multiplicative inverse of each of the complex number.

4 - 3i

175 Views

12.

Find the multiplicative inverse of each of the complex number.

$space space space space space space space space space space space space square root of 5 plus space 3 straight i$

126 Views

13.

Express the following in a + ib form.

$space space space space space space space space space space space space space space space space space space space space fraction numerator left parenthesis 3 space plus space straight i square root of 5 right parenthesis space left parenthesis 3 minus straight i square root of 5 right parenthesis end root over denominator left parenthesis square root of 3 plus square root of 2 straight i end root right parenthesis space minus space left parenthesis square root of 3 minus straight i square root of 2 right parenthesis end root end fraction$

120 Views

14.

Find the modulus and the arguments of each of the complex numbers.

$space space space space space space space space space space minus 1 minus straight i square root of 3$

132 Views

15.

Convert each of the complex numbers given in the Polar form.

$space space space space space space space space space space space space space square root of 3 plus space straight i$

114 Views

16.

Convert each of the complex numbers given in the Polar form.

-1 + i

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17.
Convert each of the complex numbers given in the Polar form.

-3

Here, z = - 3 = 3 (-1)   = $space space space space space space space space space space 3 open square brackets cosπ space plus space straight i space sinπ close square brackets$
                                = $space space space space space space space space space space straight r open parentheses cos space straight theta space plus space straight i space sin space straight theta close parentheses$

where     r =3,   $space space space space space straight theta space equals space straight pi$

i.e.    $space space space space space space space space space space space open vertical bar straight z close vertical bar equals space 3 comma space arg space left parenthesis straight z right parenthesis space equals space straight pi$