Find the value of $x$ and$y$ if $(x+iy )(2-3i) =4+i$

Important Questions on Complex Numbers and Quadratic Equations

EASY

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 5 - Complex Numbers and Quadratic Equations>SELF EVALUATION TEST>Q 1

If the roots of $x^2+16=0$ is $\pm ai$, then find the value of $a$

EASY

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 5 - Complex Numbers and Quadratic Equations>SELF EVALUATION TEST>Q 2

Find the modulus of  $4-3i$.

EASY

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 5 - Complex Numbers and Quadratic Equations>SELF EVALUATION TEST>Q 3

The sum of two numbers $x\pm iy\sqrt{5}$ is $6$ and their product is $14$, then the value of $x+y$ is

MEDIUM

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 5 - Complex Numbers and Quadratic Equations>SELF EVALUATION TEST>Q 4

If $z=2-3i,$ prove that $z^2-4z+13=0$

HARD

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 5 - Complex Numbers and Quadratic Equations>SELF EVALUATION TEST>Q 5

If the representation of the complex number $z=\frac{1-7i}{(2+i{)}^2}$ in polar form is $\sqrt{m}\left(\cos \frac{5\pi }{n}+i\sin \frac{5\pi }{n}\right)$, then find the value of $\left(m+n\right)$.

MEDIUM

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 5 - Complex Numbers and Quadratic Equations>SELF EVALUATION TEST>Q 6

If ${\left(\frac{1+i}{1-i}\right)}^{n+1}=1$, then find the least positive integer value of $n$.

MEDIUM

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 5 - Complex Numbers and Quadratic Equations>SELF EVALUATION TEST>Q 7

If $p+iq=\frac{(a-i{)}^2}{2a-i}$, show that $p^2+q^2=\frac{{\left(a^2+1\right)}^2}{4a^2+1}$

MEDIUM

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 5 - Complex Numbers and Quadratic Equations>SELF EVALUATION TEST>Q 8

The square root of $-8-6i$ is $\pm (a+ib)$, then find the value of $a+b$.