1. Definitions
For any real numbers $a$, $b$, $c$ and $d$. Let $z=a+bi$, whe… Read
Revision Note - Math - Number and Algebra - Complex Number -
2011SP-II-34
Ans: A
$\begin{array}{cl}
& 4k-\dfrac{6+ki}{i} \\
=
… Read $\begin{array}{cl}
& 4k-\dfrac{6+ki}{i} \\
=
2012-II-35
Ans: A
$\begin{array}{cl}
& i^3(\beta i-3) \\
= &
… Read $\begin{array}{cl}
& i^3(\beta i-3) \\
= &
2012PP-I-17
Ans: (a) $\dfrac{1}{5}-\dfrac{2}{5}i$ (b) (i) $p=-4$, $q
… Read 2012PP-II-34
Ans: D
$\begin{array}{cl}
& (x+3i)(3+i) \\
= & 3
… Read $\begin{array}{cl}
& (x+3i)(3+i) \\
= & 3
2013-II-36
Ans: A
$\begin{array}{cl}
& i + 2i^2+3i^3+4i^4 \\
= &#
… Read $\begin{array}{cl}
& i + 2i^2+3i^3+4i^4 \\
= &#
2014-II-36
Ans: A
$\begin{array}{cl}
& \dfrac{\beta^2 + 4}{\be
… Read $\begin{array}{cl}
& \dfrac{\beta^2 + 4}{\be
2015-II-35
Ans: C
$\begin{array}{rcl}
z & = & (a+5)i^6 + (a-
… Read $\begin{array}{rcl}
z & = & (a+5)i^6 + (a-
2016-II-34
Ans: B
I may not be true. Let $a=\pi$, which is a real number. T
… Read I may not be true. Let $a=\pi$, which is a real number. T
2017-II-35
Ans: B
$\begin{array}{rcl}
\dfrac{5}{2-i} + ki & = &#
… Read $\begin{array}{rcl}
\dfrac{5}{2-i} + ki & = &#
2018-II-37
Ans: D
$\begin{array}{cl}
& \dfrac{2i^{12} + 3i^{13
… Read $\begin{array}{cl}
& \dfrac{2i^{12} + 3i^{13
2019-II-34
Ans: D
$\begin{array}{cl}
& \dfrac{4 +i^5}{a + i}
… Read $\begin{array}{cl}
& \dfrac{4 +i^5}{a + i}
2020-II-37
Ans: C
$\begin{array}{cl}
& z_1 \\
= & \dfrac{2+
… Read $\begin{array}{cl}
& z_1 \\
= & \dfrac{2+
2021-II-35
Ans: A
… Read I must be true. For any real number $\alpha$,
$\begin{
2022-II-35
Ans: B
… Read $\begin{array}{rcl}
z & = & 4+5i^{10}-ki
2023-II-34
Ans: B
… Read $\begin{array}{cl}
& \dfrac{i}{k-i}+\dfrac