LFM Stats And Pure

turkey-yks 2016 Q27 Solving Equations for Unknown Complex Numbers View

Let z be a complex number satisfying the equality
$$i \cdot z + 1 = 2 ( 1 - \bar { z } )$$
What is the real part of the complex number z?
A) $\frac { 1 } { 6 }$
B) $\frac { 1 } { 4 }$
C) $\frac { 1 } { 2 }$
D) $\frac { 2 } { 3 }$
E) $\frac { 5 } { 6 }$

turkey-yks 2016 Q28 Powers of i or Complex Number Integer Powers View

$$( 1 + i ) ^ { 4 } \cdot \left( 2 - \frac { 2 } { i } \right) ^ { 2 }$$
What is the result of this operation?
A) $4 i$
B) 16
C) $- 32 i$
D) - 8
E) 12

turkey-yks 2017 Q23 Powers of i or Complex Number Integer Powers View

$\frac { \left( 1 - i ^ { 2 } \right) \cdot \left( 1 - i ^ { 6 } \right) \cdot \left( 1 - i ^ { 10 } \right) } { ( 1 - i ) \cdot \left( 1 - i ^ { 3 } \right) \cdot \left( 1 - i ^ { 5 } \right) }$\ What is the result of this operation?\ A) 1\ B) 2\ C) $2 + 2 i$\ D) $2 + 2 i$\ E) $1 + 2 i$

turkey-yks 2017 Q24 Solving Equations for Unknown Complex Numbers View

$4 z - 3 \bar { z } = \frac { 1 - 18 i } { 2 - i }$\ Which of the following is the complex number $z$ that satisfies this equality?\ A) $- 2 + i$\ B) $- 3 + i$\ C) $4 + 2 i$\ D) $3 - 2 i$\ E) $4 - i$

turkey-yks 2018 Q1 Complex Division/Multiplication Simplification View

Let a be a real number. In complex numbers,
$$\frac { 1 - a i } { a - i } = i$$
the equality is given.
Accordingly, what is a?
A) 4 B) 3 C) 2 D) 1 E) 0

turkey-yks 2019 Q1 Complex Division/Multiplication Simplification View

In the set of complex numbers
$$\frac { ( 4 - 2 i ) \cdot ( 6 + 3 i ) } { ( 1 - i ) \cdot ( 1 + i ) }$$
What is the result of this operation?
A) 15
B) 12
C) 10
D) 9
E) 6

turkey-yks 2020 Q10 Complex Division/Multiplication Simplification View

In the set of complex numbers
$$\frac { i \cdot ( 2 - i ) \cdot ( 2 - 4 i ) } { ( 1 - i ) \cdot ( 1 + i ) }$$
what is the result of the operation?
A) 2
B) 5
C) 10
D) $2 i$
E) $5 i$

turkey-yks 2020 Q11 Solving Equations for Unknown Complex Numbers View

Let $\bar{z}$ be the conjugate of the complex number $z$,
$$\frac { 6 + 2 i } { z } = \bar { z } + i$$
the sum of the complex numbers $z$ that satisfy the equality is what?
A) $1 + 3 i$
B) $2 + i$
C) $3 + 2 i$
D) $4 + i$

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LFM Stats And Pure

Completing the square and sketching 80

Inequalities 215

Discriminant and conditions for roots 106

Solving quadratics and applications 106

Curve Sketching 295

Factor & Remainder Theorem 90

Polynomial Division & Manipulation 44

Binomial Theorem (positive integer n) 244

Function Transformations 65

Composite & Inverse Functions 249

Partial Fractions 22

Generalised Binomial Theorem 16

Generalised Binomial Theorem and Partial Fractions 3

Complex Numbers Arithmetic 283

Complex Numbers Argand & Loci 135

Permutations & Arrangements 276

Combinations & Selection 268

Measures of Location and Spread 233

Probability Definitions 413

Tree Diagrams 5

Principle of Inclusion/Exclusion 23

Independent Events 51

Conditional Probability 127

Discrete Probability Distributions 210

Binomial Distribution 107

Geometric Distribution 11

Hypergeometric Distribution 10

Negative Binomial Distribution 2

Modelling and Hypothesis Testing 38

Hypothesis test of binomial distributions 12

Data representation 29

Continuous Probability Distributions and Random Variables 30

Continuous Uniform Random Variables 15

Geometric Probability 28

Normal Distribution 96

Approximating Binomial to Normal Distribution 7

Sign Change & Interval Methods 74

Fixed Point Iteration 12