22.11.04

TEST 1 B

Full Name:

1. Find an integer x which satisfies the following congruence

5x=3(mod 22).

Are there any more such numbers? Justify your answer. If it is possible give the general formula for such numbers.

2. The complex number
is a root of the polynomial
. Find all the other roots.

3. Solve the following equation
.

4. Knowing that

,

write the following numbers in exponential form:
,

.

5. On the complex plane find the vertexes of the square for which the diagonal is the segment beginning at point z₁ and ending at z₂ --(z₁,z₂).

6. a) Solve the equation
, where
, and I is the identity matrix.

b) Calculate the product
.

7. Using elementary row operations reduce the matrix
to row echelon form. Find the rank of A, justify your answer.

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