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Solution of a Linear Equation in Two Variables

the number of...

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the number of common solutions of equation z^n = 1 + i & z^m = 2 - i n,m belongs to N and z belongs to C

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Q. Express in the modulus and amplitude form.

\frac{(1 + i)^{2 n + 1}}{(1 - i)^{2 n - 1}}

, where n belongs to natural number.

z

be a complex number satisfying equation

z^{n} = {(¯ ¯ ¯ z)}^{m},

n, m \in N .

z

be a complex number and

c

be a real number

\geq

1 such that z +

c | z + 1 | + i = 0,

c

Q. For positive constant

r,

M

be the set of complex numbers

z

| z - 4 - 3 i | = r .

Then which of the following statements is (are) CORRECT?

A_{1}, A_{2}, A_{3}, . . ., A_{30}

be thirty sets with 5 elements and

B_{1}, B_{2}, . . ., B_{n}

n

3

C

is a set containing

m

elements such that each element of

C

belongs to exactly

10

A_{i}^{'} s

9

B_{j}^{'} s

C = 30 \cup i = 1 A_{i} = n \cup j = 1 B_{j}

, then find the number of positive integral solutions of equations of equation

x_{1} + x_{2} + . . . + x_{15} = 45

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Solution of a Linear Equation in Two Variables

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