$a+ib>c+id$ is meaningful only when

Important Questions on Complex Numbers

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>EXERCISE>Q 6

The polar form of complex number $\frac{i-1}{\cos \frac{\pi }{3}+i\sin \frac{\pi }{3}}$ is given by

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>EXERCISE>Q 7

The real values of $x$ and $y$ for which the equation $(x^4+2xi)-(3x^2+yi)=$ $(3-5i)+(1+2yi)$ is satisfied, are

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>EXERCISE>Q 8

If $a^2+b^2=1,$ then $\frac{1+b+ia}{1+b-ia}$ is equal to, (where $a, b\in R).$

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>EXERCISE>Q 9

If $z=3-4i,$ then $z^4-3z^3+3z^2+99z-95$ is equal to

EASY

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>EXERCISE>Q 10

If $z=x-iy$ and $z^{\frac{1}{3}}=p+iq,$ then $\frac{\left(\frac{x}{p}+\frac{y}{q}\right)}{p^2+q^2}$ is equal to, where $x, y, p, q\in R$

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 1

Find the value of the expression $1+i^2+i^4+i^6+i^8+\dots \dots .+i^{20}.$

EASY

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 2

Find multiplicative inverse of $3+2i$

EASY

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 3

Express $\left(\frac{1}{3}+7i\right)+(9-2i)-\left(-\frac{4}{3}+2i\right)$ in the form $a+ib.$