Find the multiplicative inverse of the complex number 4 - 3i and evaluate

Question

Asked by Abhisek | 1 year ago | 65

0 0

Class 11 Maths Complex Numbers and Quadratic Equations Add Answer

Show that 1 + i¹⁰ + i²⁰ + i³⁰ is a real number?

Solve the quadratic equations by factorization method only 6x² – 17ix – 12 = 0

Solve the quadratic equations by factorization method only x² + (1 – 2i)x – 2i = 0

Solve the quadratic equations by factorization method only x² + 10ix – 21 = 0

Solve the quadratic equations by factorization method only 17x² – 8x + 1 = 0

Accepted Answer

Let’s consider z = 4 – 3i

Then,

= 4 + 3i and

|z|² = 4² + (-3)² = 16 + 9 = 25

Thus, the multiplicative inverse of 4 – 3i is given by z^-1

\( z^{-1}=\dfrac{\overline{z}}{|z|^2}=\dfrac{4+3i}{25}=\dfrac{4}{25}+\dfrac{3}{25}i\)

Answered by Pragya Singh | 1 year ago